transversals in hypergraphs
play

Transversals in hypergraphs Anders Yeo AndersYeo@gmail.com - PowerPoint PPT Presentation

Feb 14, 2023 •571 likes •1.96k views

Transversals in hypergraphs Anders Yeo AndersYeo@gmail.com Engineering Systems and Design Singapore University of Technology and Design 8 Somapah Road 487372, Singapore Based on several papers co-authored by people such as M. A. Henning and

  1. Applications 3-SAT Colinear points in the plane. Total domination Phylogenetic trees in Biology. Feedback vertex sets (in tournaments). Coloring in hypergraphs. 2-coloring is equivalent to vertex-disjoint transversals. And many more..... Why? Anders Yeo Transversals in hypergraphs

  2. Applications 3-SAT Colinear points in the plane. Total domination Phylogenetic trees in Biology. Feedback vertex sets (in tournaments). Coloring in hypergraphs. 2-coloring is equivalent to vertex-disjoint transversals. And many more..... Why? Anders Yeo Transversals in hypergraphs

  3. Applications 3-SAT Colinear points in the plane. Total domination Phylogenetic trees in Biology. Feedback vertex sets (in tournaments). Coloring in hypergraphs. 2-coloring is equivalent to vertex-disjoint transversals. And many more..... Why? Anders Yeo Transversals in hypergraphs

  4. Applications 3-SAT Colinear points in the plane. Total domination Phylogenetic trees in Biology. Feedback vertex sets (in tournaments). Coloring in hypergraphs. 2-coloring is equivalent to vertex-disjoint transversals. And many more..... Why? Anders Yeo Transversals in hypergraphs

  5. Applications 3-SAT Colinear points in the plane. Total domination Phylogenetic trees in Biology. Feedback vertex sets (in tournaments). Coloring in hypergraphs. 2-coloring is equivalent to vertex-disjoint transversals. And many more..... Why? Anders Yeo Transversals in hypergraphs

  6. Applications 3-SAT Colinear points in the plane. Total domination Phylogenetic trees in Biology. Feedback vertex sets (in tournaments). Coloring in hypergraphs. 2-coloring is equivalent to vertex-disjoint transversals. And many more..... Why? Anders Yeo Transversals in hypergraphs

  7. Applications 3-SAT Colinear points in the plane. Total domination Phylogenetic trees in Biology. Feedback vertex sets (in tournaments). Coloring in hypergraphs. 2-coloring is equivalent to vertex-disjoint transversals. And many more..... Why? Anders Yeo Transversals in hypergraphs

  8. Applications 3-SAT Colinear points in the plane. Total domination Phylogenetic trees in Biology. Feedback vertex sets (in tournaments). Coloring in hypergraphs. 2-coloring is equivalent to vertex-disjoint transversals. And many more..... Why? Anders Yeo Transversals in hypergraphs

  9. 3 -SAT Consider an instance, I , of 3-SAT with n vriables and m clauses. For example, I = ( v 1 ∨ v 2 ∨ v 3 ) ∧ ( v 2 ∨ v 3 ∨ v 4 ) ∧ · · · . v 1 v 2 v 3 v 4 v 5 v n · · · v 1 v 2 v 3 v 4 v 5 v n We build a hypergraph, H , with 2 n vertices as above. Each variable gives rise to a 2-edge. Each clause gives rise to a 3-edge. H has a transversal of size n if and only if I is satisfiable. We believe this reduction may be used to improve currently best algorithms for 3-SAT. Anders Yeo Transversals in hypergraphs

  10. 3 -SAT Consider an instance, I , of 3-SAT with n vriables and m clauses. For example, I = ( v 1 ∨ v 2 ∨ v 3 ) ∧ ( v 2 ∨ v 3 ∨ v 4 ) ∧ · · · . v 1 v 2 v 3 v 4 v 5 v n · · · v 1 v 2 v 3 v 4 v 5 v n We build a hypergraph, H , with 2 n vertices as above. Each variable gives rise to a 2-edge. Each clause gives rise to a 3-edge. H has a transversal of size n if and only if I is satisfiable. We believe this reduction may be used to improve currently best algorithms for 3-SAT. Anders Yeo Transversals in hypergraphs

  11. 3 -SAT Consider an instance, I , of 3-SAT with n vriables and m clauses. For example, I = ( v 1 ∨ v 2 ∨ v 3 ) ∧ ( v 2 ∨ v 3 ∨ v 4 ) ∧ · · · . v 1 v 2 v 3 v 4 v 5 v n · · · v 1 v 2 v 3 v 4 v 5 v n We build a hypergraph, H , with 2 n vertices as above. Each variable gives rise to a 2-edge. Each clause gives rise to a 3-edge. H has a transversal of size n if and only if I is satisfiable. We believe this reduction may be used to improve currently best algorithms for 3-SAT. Anders Yeo Transversals in hypergraphs

  12. 3 -SAT Consider an instance, I , of 3-SAT with n vriables and m clauses. For example, I = ( v 1 ∨ v 2 ∨ v 3 ) ∧ ( v 2 ∨ v 3 ∨ v 4 ) ∧ · · · . v 1 v 2 v 3 v 4 v 5 v n · · · v 1 v 2 v 3 v 4 v 5 v n We build a hypergraph, H , with 2 n vertices as above. Each variable gives rise to a 2-edge. Each clause gives rise to a 3-edge. H has a transversal of size n if and only if I is satisfiable. We believe this reduction may be used to improve currently best algorithms for 3-SAT. Anders Yeo Transversals in hypergraphs

  13. 3 -SAT Consider an instance, I , of 3-SAT with n vriables and m clauses. For example, I = ( v 1 ∨ v 2 ∨ v 3 ) ∧ ( v 2 ∨ v 3 ∨ v 4 ) ∧ · · · . v 1 v 2 v 3 v 4 v 5 v n · · · v 1 v 2 v 3 v 4 v 5 v n We build a hypergraph, H , with 2 n vertices as above. Each variable gives rise to a 2-edge. Each clause gives rise to a 3-edge. H has a transversal of size n if and only if I is satisfiable. We believe this reduction may be used to improve currently best algorithms for 3-SAT. Anders Yeo Transversals in hypergraphs

  14. 3 -SAT Consider an instance, I , of 3-SAT with n vriables and m clauses. For example, I = ( v 1 ∨ v 2 ∨ v 3 ) ∧ ( v 2 ∨ v 3 ∨ v 4 ) ∧ · · · . v 1 v 2 v 3 v 4 v 5 v n · · · v 1 v 2 v 3 v 4 v 5 v n We build a hypergraph, H , with 2 n vertices as above. Each variable gives rise to a 2-edge. Each clause gives rise to a 3-edge. H has a transversal of size n if and only if I is satisfiable. We believe this reduction may be used to improve currently best algorithms for 3-SAT. Anders Yeo Transversals in hypergraphs

  15. 3 -SAT Consider an instance, I , of 3-SAT with n vriables and m clauses. For example, I = ( v 1 ∨ v 2 ∨ v 3 ) ∧ ( v 2 ∨ v 3 ∨ v 4 ) ∧ · · · . v 1 v 2 v 3 v 4 v 5 v n · · · v 1 v 2 v 3 v 4 v 5 v n We build a hypergraph, H , with 2 n vertices as above. Each variable gives rise to a 2-edge. Each clause gives rise to a 3-edge. H has a transversal of size n if and only if I is satisfiable. We believe this reduction may be used to improve currently best algorithms for 3-SAT. Anders Yeo Transversals in hypergraphs

  16. Colinear points in the plane We are given a number of points in the plane. Can we find the largest set of points where no 3 are co-linear (lie on a line)? Add 3-edges between all sets of 3 points that are colinear. Remove the points of a minimum transversal. If no four points are co-linear then the resulting hypergraph is linear. Anders Yeo Transversals in hypergraphs

  17. Colinear points in the plane We are given a number of points in the plane. Can we find the largest set of points where no 3 are co-linear (lie on a line)? Add 3-edges between all sets of 3 points that are colinear. Remove the points of a minimum transversal. If no four points are co-linear then the resulting hypergraph is linear. Anders Yeo Transversals in hypergraphs

  18. Colinear points in the plane We are given a number of points in the plane. Can we find the largest set of points where no 3 are co-linear (lie on a line)? Add 3-edges between all sets of 3 points that are colinear. Remove the points of a minimum transversal. If no four points are co-linear then the resulting hypergraph is linear. Anders Yeo Transversals in hypergraphs

  19. Colinear points in the plane We are given a number of points in the plane. Can we find the largest set of points where no 3 are co-linear (lie on a line)? Add 3-edges between all sets of 3 points that are colinear. Remove the points of a minimum transversal. If no four points are co-linear then the resulting hypergraph is linear. Anders Yeo Transversals in hypergraphs

  20. Colinear points in the plane We are given a number of points in the plane. Can we find the largest set of points where no 3 are co-linear (lie on a line)? Add 3-edges between all sets of 3 points that are colinear. Remove the points of a minimum transversal. If no four points are co-linear then the resulting hypergraph is linear. Anders Yeo Transversals in hypergraphs

  21. Colinear points in the plane We are given a number of points in the plane. Can we find the largest set of points where no 3 are co-linear (lie on a line)? Add 3-edges between all sets of 3 points that are colinear. Remove the points of a minimum transversal. If no four points are co-linear then the resulting hypergraph is linear. Anders Yeo Transversals in hypergraphs

  22. Colinear points in the plane We are given a number of points in the plane. Can we find the largest set of points where no 3 are co-linear (lie on a line)? Add 3-edges between all sets of 3 points that are colinear. Remove the points of a minimum transversal. If no four points are co-linear then the resulting hypergraph is linear. Anders Yeo Transversals in hypergraphs

  23. Total Domination S is a total dominating set in G , if and only if every vertex in G has a neighbour in S . v 1 v 2 v 3 u 4 u 5 v 6 v 5 v 4 u 1 u 2 u 3 G ′ G γ t ( G ) denotes the size of a smallest total dominating set in G . Anders Yeo Transversals in hypergraphs

  24. Total Domination S is a total dominating set in G , if and only if every vertex in G has a neighbour in S . v 1 v 2 v 3 u 4 u 5 v 6 v 5 v 4 u 1 u 2 u 3 G ′ G γ t ( G ) denotes the size of a smallest total dominating set in G . Anders Yeo Transversals in hypergraphs

  25. Total Domination S is a total dominating set in G , if and only if every vertex in G has a neighbour in S . v 1 v 2 v 3 u 4 u 5 v 6 v 5 v 4 u 1 u 2 u 3 G ′ G γ t ( G ) denotes the size of a smallest total dominating set in G . Anders Yeo Transversals in hypergraphs

  26. Total Domination S is a total dominating set in G , if and only if every vertex in G has a neighbour in S . v 1 v 2 v 3 u 4 u 5 v 6 v 5 v 4 u 1 u 2 u 3 G ′ G γ t ( G ) denotes the size of a smallest total dominating set in G . Anders Yeo Transversals in hypergraphs

  27. Total Domination S is a total dominating set in G , if and only if every vertex in G has a neighbour in S . v 1 v 2 v 3 u 4 u 5 v 6 v 5 v 4 u 1 u 2 u 3 G ′ G γ t ( G ) denotes the size of a smallest total dominating set in G . Anders Yeo Transversals in hypergraphs

  28. Total Domination S is a total dominating set in G , if and only if every vertex in G has a neighbour in S . v 1 v 2 v 3 u 4 u 5 v 6 v 5 v 4 u 1 u 2 u 3 G ′ G γ t ( G ) denotes the size of a smallest total dominating set in G . Anders Yeo Transversals in hypergraphs

  29. Total Domination S is a total dominating set in G , if and only if every vertex in G has a neighbour in S . v 1 v 2 v 3 u 4 u 5 v 6 v 5 v 4 u 1 u 2 u 3 G ′ G γ t ( G ) denotes the size of a smallest total dominating set in G . Anders Yeo Transversals in hypergraphs

  30. Total Domination S is a total dominating set in G , if and only if every vertex in G has a neighbour in S . v 1 v 2 v 3 u 4 u 5 v 6 v 5 v 4 u 1 u 2 u 3 G ′ G γ t ( G ) denotes the size of a smallest total dominating set in G . Anders Yeo Transversals in hypergraphs

  31. Total Domination, Open Neighbourhood hypergraph Given G , the Open Neighbourhood Hypergraph, ONH ( G ), of G has vertex-set V ( G ) and edge-set { N ( v ) | v ∈ V ( G ) } . u 4 u 5 u 4 u 5 u 1 u 2 u 3 u 1 u 2 u 3 ONH ( G ) G A transversal in ONH ( G ) is equivalent to a total dominating set in G . Most recent results on Total Domination are found using transversals in hypergraphs. Anders Yeo Transversals in hypergraphs

  32. Total Domination, Open Neighbourhood hypergraph Given G , the Open Neighbourhood Hypergraph, ONH ( G ), of G has vertex-set V ( G ) and edge-set { N ( v ) | v ∈ V ( G ) } . u 4 u 5 u 4 u 5 u 1 u 2 u 3 u 1 u 2 u 3 ONH ( G ) G A transversal in ONH ( G ) is equivalent to a total dominating set in G . Most recent results on Total Domination are found using transversals in hypergraphs. Anders Yeo Transversals in hypergraphs

  33. Total Domination, Open Neighbourhood hypergraph Given G , the Open Neighbourhood Hypergraph, ONH ( G ), of G has vertex-set V ( G ) and edge-set { N ( v ) | v ∈ V ( G ) } . u 4 u 5 u 4 u 5 u 1 u 2 u 3 u 1 u 2 u 3 ONH ( G ) G A transversal in ONH ( G ) is equivalent to a total dominating set in G . Most recent results on Total Domination are found using transversals in hypergraphs. Anders Yeo Transversals in hypergraphs

  34. Total Domination, Open Neighbourhood hypergraph Given G , the Open Neighbourhood Hypergraph, ONH ( G ), of G has vertex-set V ( G ) and edge-set { N ( v ) | v ∈ V ( G ) } . u 4 u 5 u 4 u 5 u 1 u 2 u 3 u 1 u 2 u 3 ONH ( G ) G A transversal in ONH ( G ) is equivalent to a total dominating set in G . Most recent results on Total Domination are found using transversals in hypergraphs. Anders Yeo Transversals in hypergraphs

  35. Total Domination, Open Neighbourhood hypergraph Given G , the Open Neighbourhood Hypergraph, ONH ( G ), of G has vertex-set V ( G ) and edge-set { N ( v ) | v ∈ V ( G ) } . u 4 u 5 u 4 u 5 u 1 u 2 u 3 u 1 u 2 u 3 ONH ( G ) G A transversal in ONH ( G ) is equivalent to a total dominating set in G . Most recent results on Total Domination are found using transversals in hypergraphs. Anders Yeo Transversals in hypergraphs

  36. Total Domination, Open Neighbourhood hypergraph Given G , the Open Neighbourhood Hypergraph, ONH ( G ), of G has vertex-set V ( G ) and edge-set { N ( v ) | v ∈ V ( G ) } . u 4 u 5 u 4 u 5 u 1 u 2 u 3 u 1 u 2 u 3 ONH ( G ) G A transversal in ONH ( G ) is equivalent to a total dominating set in G . Most recent results on Total Domination are found using transversals in hypergraphs. Anders Yeo Transversals in hypergraphs

  37. Total Domination, Open Neighbourhood hypergraph Given G , the Open Neighbourhood Hypergraph, ONH ( G ), of G has vertex-set V ( G ) and edge-set { N ( v ) | v ∈ V ( G ) } . u 4 u 5 u 4 u 5 u 1 u 2 u 3 u 1 u 2 u 3 ONH ( G ) G A transversal in ONH ( G ) is equivalent to a total dominating set in G . Most recent results on Total Domination are found using transversals in hypergraphs. Anders Yeo Transversals in hypergraphs

  38. Total Domination, Open Neighbourhood hypergraph Given G , the Open Neighbourhood Hypergraph, ONH ( G ), of G has vertex-set V ( G ) and edge-set { N ( v ) | v ∈ V ( G ) } . u 4 u 5 u 4 u 5 u 1 u 2 u 3 u 1 u 2 u 3 ONH ( G ) G A transversal in ONH ( G ) is equivalent to a total dominating set in G . Most recent results on Total Domination are found using transversals in hypergraphs. Anders Yeo Transversals in hypergraphs

  39. More.... In Phylogenetic trees we want to remove as few species as possible such that the known Phylogenetic trees dont contradict each other. This can be modelled as a transversal problem in 3-uniform hypergraphs. Feedback vertex sets (in tournaments). Given a graph or digraph put a hyperdege around the vertex set of all chordless cycles. A transversal in the resulting hypergraph is a minimum feedback vertex set. For tournaments all chordless cycles are 3-cycles so our hypergraph is 3-uniform. We have best known algorithms for both the above using transversals in hypergraphs. Anders Yeo Transversals in hypergraphs

  40. More.... In Phylogenetic trees we want to remove as few species as possible such that the known Phylogenetic trees dont contradict each other. This can be modelled as a transversal problem in 3-uniform hypergraphs. Feedback vertex sets (in tournaments). Given a graph or digraph put a hyperdege around the vertex set of all chordless cycles. A transversal in the resulting hypergraph is a minimum feedback vertex set. For tournaments all chordless cycles are 3-cycles so our hypergraph is 3-uniform. We have best known algorithms for both the above using transversals in hypergraphs. Anders Yeo Transversals in hypergraphs

  41. More.... In Phylogenetic trees we want to remove as few species as possible such that the known Phylogenetic trees dont contradict each other. This can be modelled as a transversal problem in 3-uniform hypergraphs. Feedback vertex sets (in tournaments). Given a graph or digraph put a hyperdege around the vertex set of all chordless cycles. A transversal in the resulting hypergraph is a minimum feedback vertex set. For tournaments all chordless cycles are 3-cycles so our hypergraph is 3-uniform. We have best known algorithms for both the above using transversals in hypergraphs. Anders Yeo Transversals in hypergraphs

  42. Known results and conjectures, order and size For connected k -uniform hypergraphs there are bounds just based on the order, n , and size, m . os & Tuza) If k = 2 then τ ( H ) ≤ 2( n + m +1) (Erd¨ . 7 atal & McDiarmid) If k ≥ 2 then τ ( H ) ≤ n + ⌊ k / 2 ⌋ m (Chv´ ⌊ 3 k / 2 ⌋ . The above bounds are tight for hy- k 2 n = 3 k / 2 pergraphs of average degree 2. m = 3 For larger average degrees not τ = 2 k k much is known. 2 2 The following is tight for average degrees 3-4. e & Yeo) If k = 4 then τ ( H ) ≤ 5 n +4 m (Thomass´ . 21 Anders Yeo Transversals in hypergraphs

  43. Known results and conjectures, order and size For connected k -uniform hypergraphs there are bounds just based on the order, n , and size, m . os & Tuza) If k = 2 then τ ( H ) ≤ 2( n + m +1) (Erd¨ . 7 atal & McDiarmid) If k ≥ 2 then τ ( H ) ≤ n + ⌊ k / 2 ⌋ m (Chv´ ⌊ 3 k / 2 ⌋ . The above bounds are tight for hy- k 2 n = 3 k / 2 pergraphs of average degree 2. m = 3 For larger average degrees not τ = 2 k k much is known. 2 2 The following is tight for average degrees 3-4. e & Yeo) If k = 4 then τ ( H ) ≤ 5 n +4 m (Thomass´ . 21 Anders Yeo Transversals in hypergraphs

  44. Known results and conjectures, order and size For connected k -uniform hypergraphs there are bounds just based on the order, n , and size, m . os & Tuza) If k = 2 then τ ( H ) ≤ 2( n + m +1) (Erd¨ . 7 atal & McDiarmid) If k ≥ 2 then τ ( H ) ≤ n + ⌊ k / 2 ⌋ m (Chv´ ⌊ 3 k / 2 ⌋ . The above bounds are tight for hy- k 2 n = 3 k / 2 pergraphs of average degree 2. m = 3 For larger average degrees not τ = 2 k k much is known. 2 2 The following is tight for average degrees 3-4. e & Yeo) If k = 4 then τ ( H ) ≤ 5 n +4 m (Thomass´ . 21 Anders Yeo Transversals in hypergraphs

  45. Known results and conjectures, order and size For connected k -uniform hypergraphs there are bounds just based on the order, n , and size, m . os & Tuza) If k = 2 then τ ( H ) ≤ 2( n + m +1) (Erd¨ . 7 atal & McDiarmid) If k ≥ 2 then τ ( H ) ≤ n + ⌊ k / 2 ⌋ m (Chv´ ⌊ 3 k / 2 ⌋ . The above bounds are tight for hy- k 2 n = 3 k / 2 pergraphs of average degree 2. m = 3 For larger average degrees not τ = 2 k k much is known. 2 2 The following is tight for average degrees 3-4. e & Yeo) If k = 4 then τ ( H ) ≤ 5 n +4 m (Thomass´ . 21 Anders Yeo Transversals in hypergraphs

  46. Known results and conjectures, corollaries Given the results on the previous slide, we automatically get results for total domination in graphs with given minimum degree. If k = 3 and n = m then τ ( H ) ≤ n / 2. So, γ t ( G ) ≤ n / 4 when δ ( G ) ≥ 3. If k = 4 and n = m then τ ( H ) ≤ 3 n / 7. So, γ t ( G ) ≤ 3 n / 7 when δ ( G ) ≥ 4. Conjecture: If k = 5 and n = m then τ ( H ) ≤ 4 n / 11. The above conjecture would be best possible. Open Problem: For k ≥ 4 prove better bounds for linear hypergraphs. Anders Yeo Transversals in hypergraphs

  47. Known results and conjectures, corollaries Given the results on the previous slide, we automatically get results for total domination in graphs with given minimum degree. If k = 3 and n = m then τ ( H ) ≤ n / 2. So, γ t ( G ) ≤ n / 4 when δ ( G ) ≥ 3. If k = 4 and n = m then τ ( H ) ≤ 3 n / 7. So, γ t ( G ) ≤ 3 n / 7 when δ ( G ) ≥ 4. Conjecture: If k = 5 and n = m then τ ( H ) ≤ 4 n / 11. The above conjecture would be best possible. Open Problem: For k ≥ 4 prove better bounds for linear hypergraphs. Anders Yeo Transversals in hypergraphs

  48. Known results and conjectures, corollaries Given the results on the previous slide, we automatically get results for total domination in graphs with given minimum degree. If k = 3 and n = m then τ ( H ) ≤ n / 2. So, γ t ( G ) ≤ n / 4 when δ ( G ) ≥ 3. If k = 4 and n = m then τ ( H ) ≤ 3 n / 7. So, γ t ( G ) ≤ 3 n / 7 when δ ( G ) ≥ 4. Conjecture: If k = 5 and n = m then τ ( H ) ≤ 4 n / 11. The above conjecture would be best possible. Open Problem: For k ≥ 4 prove better bounds for linear hypergraphs. Anders Yeo Transversals in hypergraphs

  49. Known results and conjectures, corollaries Given the results on the previous slide, we automatically get results for total domination in graphs with given minimum degree. If k = 3 and n = m then τ ( H ) ≤ n / 2. So, γ t ( G ) ≤ n / 4 when δ ( G ) ≥ 3. If k = 4 and n = m then τ ( H ) ≤ 3 n / 7. So, γ t ( G ) ≤ 3 n / 7 when δ ( G ) ≥ 4. Conjecture: If k = 5 and n = m then τ ( H ) ≤ 4 n / 11. The above conjecture would be best possible. Open Problem: For k ≥ 4 prove better bounds for linear hypergraphs. Anders Yeo Transversals in hypergraphs

  50. Known results and conjectures, corollaries Given the results on the previous slide, we automatically get results for total domination in graphs with given minimum degree. If k = 3 and n = m then τ ( H ) ≤ n / 2. So, γ t ( G ) ≤ n / 4 when δ ( G ) ≥ 3. If k = 4 and n = m then τ ( H ) ≤ 3 n / 7. So, γ t ( G ) ≤ 3 n / 7 when δ ( G ) ≥ 4. Conjecture: If k = 5 and n = m then τ ( H ) ≤ 4 n / 11. The above conjecture would be best possible. Open Problem: For k ≥ 4 prove better bounds for linear hypergraphs. Anders Yeo Transversals in hypergraphs

  51. Known results and conjectures, corollaries Given the results on the previous slide, we automatically get results for total domination in graphs with given minimum degree. If k = 3 and n = m then τ ( H ) ≤ n / 2. So, γ t ( G ) ≤ n / 4 when δ ( G ) ≥ 3. If k = 4 and n = m then τ ( H ) ≤ 3 n / 7. So, γ t ( G ) ≤ 3 n / 7 when δ ( G ) ≥ 4. Conjecture: If k = 5 and n = m then τ ( H ) ≤ 4 n / 11. The above conjecture would be best possible. Open Problem: For k ≥ 4 prove better bounds for linear hypergraphs. Anders Yeo Transversals in hypergraphs

  52. Known results and conjectures, regularity Very little is known regarding the regularity of a hypergraphs and the following has been conjectured. Conjecture For all k ≥ 2, if H is a k -uniform hypergraph, then the following holds. (a) If H is 3-regular then τ ( H ) ≤ 3 n 2 k (holds for k ≤ 4). (b) If H is 4-regular then τ ( H ) ≤ 12 n 7 k (holds for k ≤ 4). (c) If H is 5-regular then τ ( H ) ≤ 20 n 11 k (holds for k ≤ 3). (d) If H is 6-regular then τ ( H ) ≤ 24 n 13 k (holds for k ≤ 2). We now believe we have a proof of (a) for when k = 6. That is we can prove, Tuza-Vestergaard Conjecture (Now proved?): Every 3-regular 6-uniform hypergraph, H , satisfies τ ( H ) ≤ | V ( H ) | / 4. Anders Yeo Transversals in hypergraphs

  53. Known results and conjectures, regularity Very little is known regarding the regularity of a hypergraphs and the following has been conjectured. Conjecture For all k ≥ 2, if H is a k -uniform hypergraph, then the following holds. (a) If H is 3-regular then τ ( H ) ≤ 3 n 2 k (holds for k ≤ 4). (b) If H is 4-regular then τ ( H ) ≤ 12 n 7 k (holds for k ≤ 4). (c) If H is 5-regular then τ ( H ) ≤ 20 n 11 k (holds for k ≤ 3). (d) If H is 6-regular then τ ( H ) ≤ 24 n 13 k (holds for k ≤ 2). We now believe we have a proof of (a) for when k = 6. That is we can prove, Tuza-Vestergaard Conjecture (Now proved?): Every 3-regular 6-uniform hypergraph, H , satisfies τ ( H ) ≤ | V ( H ) | / 4. Anders Yeo Transversals in hypergraphs

  54. Known results and conjectures, regularity Very little is known regarding the regularity of a hypergraphs and the following has been conjectured. Conjecture For all k ≥ 2, if H is a k -uniform hypergraph, then the following holds. (a) If H is 3-regular then τ ( H ) ≤ 3 n 2 k (holds for k ≤ 4). (b) If H is 4-regular then τ ( H ) ≤ 12 n 7 k (holds for k ≤ 4). (c) If H is 5-regular then τ ( H ) ≤ 20 n 11 k (holds for k ≤ 3). (d) If H is 6-regular then τ ( H ) ≤ 24 n 13 k (holds for k ≤ 2). We now believe we have a proof of (a) for when k = 6. That is we can prove, Tuza-Vestergaard Conjecture (Now proved?): Every 3-regular 6-uniform hypergraph, H , satisfies τ ( H ) ≤ | V ( H ) | / 4. Anders Yeo Transversals in hypergraphs

  55. Known results and conjectures, regularity Very little is known regarding the regularity of a hypergraphs and the following has been conjectured. Conjecture For all k ≥ 2, if H is a k -uniform hypergraph, then the following holds. (a) If H is 3-regular then τ ( H ) ≤ 3 n 2 k (holds for k ≤ 4). (b) If H is 4-regular then τ ( H ) ≤ 12 n 7 k (holds for k ≤ 4). (c) If H is 5-regular then τ ( H ) ≤ 20 n 11 k (holds for k ≤ 3). (d) If H is 6-regular then τ ( H ) ≤ 24 n 13 k (holds for k ≤ 2). We now believe we have a proof of (a) for when k = 6. That is we can prove, Tuza-Vestergaard Conjecture (Now proved?): Every 3-regular 6-uniform hypergraph, H , satisfies τ ( H ) ≤ | V ( H ) | / 4. Anders Yeo Transversals in hypergraphs

  56. Progress on the Tuza-Vestergaard Conjecture The well-known Tuza-Vestergaard conjecture was published in 2002. Bounds of 0 . 27778 n , 0 . 27037 n and 0 . 268116 n have been showed. There are infinitely many hypergraphs achieving equality in the bound n / 4. (Take any 3-regular 3-uniform hyper- graph, H , with τ ( H ) = n / 2 and du- plicate every vertex). Our proof of the Tuza-Vestergaard conjecture also implies a number of other results. For example, the following for k = 6. Conjecture: For all k ≥ 2, if H is a k -uniform hypergraph with maximum degree ∆( H ) ≤ 3 then τ ( H ) ≤ | V ( H ) | + | E ( H ) | . 6 k Anders Yeo Transversals in hypergraphs

  57. Progress on the Tuza-Vestergaard Conjecture The well-known Tuza-Vestergaard conjecture was published in 2002. Bounds of 0 . 27778 n , 0 . 27037 n and 0 . 268116 n have been showed. There are infinitely many hypergraphs achieving equality in the bound n / 4. (Take any 3-regular 3-uniform hyper- graph, H , with τ ( H ) = n / 2 and du- plicate every vertex). Our proof of the Tuza-Vestergaard conjecture also implies a number of other results. For example, the following for k = 6. Conjecture: For all k ≥ 2, if H is a k -uniform hypergraph with maximum degree ∆( H ) ≤ 3 then τ ( H ) ≤ | V ( H ) | + | E ( H ) | . 6 k Anders Yeo Transversals in hypergraphs

  58. Progress on the Tuza-Vestergaard Conjecture The well-known Tuza-Vestergaard conjecture was published in 2002. Bounds of 0 . 27778 n , 0 . 27037 n and 0 . 268116 n have been showed. There are infinitely many hypergraphs achieving equality in the bound n / 4. (Take any 3-regular 3-uniform hyper- graph, H , with τ ( H ) = n / 2 and du- plicate every vertex). Our proof of the Tuza-Vestergaard conjecture also implies a number of other results. For example, the following for k = 6. Conjecture: For all k ≥ 2, if H is a k -uniform hypergraph with maximum degree ∆( H ) ≤ 3 then τ ( H ) ≤ | V ( H ) | + | E ( H ) | . 6 k Anders Yeo Transversals in hypergraphs

  59. Progress on the Tuza-Vestergaard Conjecture The well-known Tuza-Vestergaard conjecture was published in 2002. Bounds of 0 . 27778 n , 0 . 27037 n and 0 . 268116 n have been showed. There are infinitely many hypergraphs achieving equality in the bound n / 4. (Take any 3-regular 3-uniform hyper- graph, H , with τ ( H ) = n / 2 and du- plicate every vertex). Our proof of the Tuza-Vestergaard conjecture also implies a number of other results. For example, the following for k = 6. Conjecture: For all k ≥ 2, if H is a k -uniform hypergraph with maximum degree ∆( H ) ≤ 3 then τ ( H ) ≤ | V ( H ) | + | E ( H ) | . 6 k Anders Yeo Transversals in hypergraphs

  60. Progress on the Tuza-Vestergaard Conjecture The well-known Tuza-Vestergaard conjecture was published in 2002. Bounds of 0 . 27778 n , 0 . 27037 n and 0 . 268116 n have been showed. There are infinitely many hypergraphs achieving equality in the bound n / 4. (Take any 3-regular 3-uniform hyper- graph, H , with τ ( H ) = n / 2 and du- plicate every vertex). Our proof of the Tuza-Vestergaard conjecture also implies a number of other results. For example, the following for k = 6. Conjecture: For all k ≥ 2, if H is a k -uniform hypergraph with maximum degree ∆( H ) ≤ 3 then τ ( H ) ≤ | V ( H ) | + | E ( H ) | . 6 k Anders Yeo Transversals in hypergraphs

  61. Progress on the Tuza-Vestergaard Conjecture In order to prove the Tuza-Vestergaard Conjecture we prove a much stronger result. If H is a 6-uniform hypergraph on n vertices and m edges with ∆( H ) ≤ 3, then 20 τ ( H ) ≤ 2 n + 6 m + ρ , where ρ is a number that depends on the existence of certain hypergraphs, which will be described in more detail below. SB 1 B 1 B 2 B 3 B 4 Anders Yeo Transversals in hypergraphs

  62. Progress on the Tuza-Vestergaard Conjecture In order to prove the Tuza-Vestergaard Conjecture we prove a much stronger result. If H is a 6-uniform hypergraph on n vertices and m edges with ∆( H ) ≤ 3, then 20 τ ( H ) ≤ 2 n + 6 m + ρ , where ρ is a number that depends on the existence of certain hypergraphs, which will be described in more detail below. SB 1 B 1 B 2 B 3 B 4 Anders Yeo Transversals in hypergraphs

  63. Progress on the Tuza-Vestergaard Conjecture We recusively define an infinite family B of bad hypergraphs as follows. Let B = { B 1 , B 2 , B 3 , B 4 } and recursively do the following.... No minimum transversal contains a red and green In B → vertex. Any hypergraph in B is 2 short in the formula 20 τ ≤ 2 n + 6 m . What about SB 1 ? Anders Yeo Transversals in hypergraphs

  64. Progress on the Tuza-Vestergaard Conjecture We recusively define an infinite family B of bad hypergraphs as follows. Let B = { B 1 , B 2 , B 3 , B 4 } and recursively do the following.... No minimum transversal contains a red and green In B → vertex. Any hypergraph in B is 2 short in the formula 20 τ ≤ 2 n + 6 m . What about SB 1 ? Anders Yeo Transversals in hypergraphs

  65. Progress on the Tuza-Vestergaard Conjecture We recusively define an infinite family B of bad hypergraphs as follows. Let B = { B 1 , B 2 , B 3 , B 4 } and recursively do the following.... No minimum transversal contains a red and green In B → vertex. Any hypergraph in B is 2 short in the formula 20 τ ≤ 2 n + 6 m . What about SB 1 ? Anders Yeo Transversals in hypergraphs

  66. Progress on the Tuza-Vestergaard Conjecture We recusively define an infinite family B of bad hypergraphs as follows. Let B = { B 1 , B 2 , B 3 , B 4 } and recursively do the following.... No minimum transversal contains a red and green In B → vertex. Any hypergraph in B is 2 short in the formula 20 τ ≤ 2 n + 6 m . What about SB 1 ? Anders Yeo Transversals in hypergraphs

  67. Progress on the Tuza-Vestergaard Conjecture We recusively define an infinite family B of bad hypergraphs as follows. Let B = { B 1 , B 2 , B 3 , B 4 } and recursively do the following.... No minimum transversal contains a red and green In B → vertex. Any hypergraph in B is 2 short in the formula 20 τ ≤ 2 n + 6 m . What about SB 1 ? Anders Yeo Transversals in hypergraphs

  68. Progress on the Tuza-Vestergaard Conjecture We recusively define an infinite family B of bad hypergraphs as follows. Let B = { B 1 , B 2 , B 3 , B 4 } and recursively do the following.... No minimum transversal contains a red and green In B → vertex. Any hypergraph in B is 2 short in the formula 20 τ ≤ 2 n + 6 m . What about SB 1 ? Anders Yeo Transversals in hypergraphs

  69. Progress on the Tuza-Vestergaard Conjecture We recusively define an infinite family B of bad hypergraphs as follows. Let B = { B 1 , B 2 , B 3 , B 4 } and recursively do the following.... No minimum transversal contains a red and green In B → vertex. Any hypergraph in B is 2 short in the formula 20 τ ≤ 2 n + 6 m . What about SB 1 ? Anders Yeo Transversals in hypergraphs

  70. Progress on the Tuza-Vestergaard Conjecture We recusively define an infinite family B of bad hypergraphs as follows. Let B = { B 1 , B 2 , B 3 , B 4 } and recursively do the following.... No minimum transversal contains a red and green In B → vertex. Any hypergraph in B is 2 short in the formula 20 τ ≤ 2 n + 6 m . What about SB 1 ? Anders Yeo Transversals in hypergraphs

  71. Progress on the Tuza-Vestergaard Conjecture SB 1 is 4 short in the formula 20 τ ≤ 2 n + 6 m . If C is a SB 1 subgraph in H , then define f ( C ) as follows: # degree 2’s in C 0 1 2 3 4 5 6 7 8 9 f ( C ) 0 0 0 1 1 1 2 2 3 4  2 R is a component in H  If R ∈ B then f ( R ) = 1 R is intersected by 1 edge . 0 R is intersected by ≥ 2 edges  Let ρ = max � Q ∈Q f ( Q ) over all families of vertex-disjoint subgraphs Q in H ( F ( Q ) = 0 if Q �∈ B ∪ SB 1 ). Anders Yeo Transversals in hypergraphs

  72. Progress on the Tuza-Vestergaard Conjecture SB 1 is 4 short in the formula 20 τ ≤ 2 n + 6 m . If C is a SB 1 subgraph in H , then define f ( C ) as follows: # degree 2’s in C 0 1 2 3 4 5 6 7 8 9 f ( C ) 0 0 0 1 1 1 2 2 3 4  2 R is a component in H  If R ∈ B then f ( R ) = 1 R is intersected by 1 edge . 0 R is intersected by ≥ 2 edges  Let ρ = max � Q ∈Q f ( Q ) over all families of vertex-disjoint subgraphs Q in H ( F ( Q ) = 0 if Q �∈ B ∪ SB 1 ). Anders Yeo Transversals in hypergraphs

  73. Progress on the Tuza-Vestergaard Conjecture SB 1 is 4 short in the formula 20 τ ≤ 2 n + 6 m . If C is a SB 1 subgraph in H , then define f ( C ) as follows: # degree 2’s in C 0 1 2 3 4 5 6 7 8 9 f ( C ) 0 0 0 1 1 1 2 2 3 4  2 R is a component in H  If R ∈ B then f ( R ) = 1 R is intersected by 1 edge . 0 R is intersected by ≥ 2 edges  Let ρ = max � Q ∈Q f ( Q ) over all families of vertex-disjoint subgraphs Q in H ( F ( Q ) = 0 if Q �∈ B ∪ SB 1 ). Anders Yeo Transversals in hypergraphs

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Transversals and Domination in Hypergraphs Michael A. Henning Department of Mathematics

Transversals and Domination in Hypergraphs Michael A. Henning Department of Mathematics

Transversals and Domination in Hypergraphs Michael A. Henning Department of Mathematics University of Johannesburg 24th Cumberland Conference 12 May 2011 1/50 Michael A. Henning Transversals and Domination in Hypergraphs Hypergraphs

1.68k views • 129 slides
Hypergraphs in Chaos JULIUS LISCHEID Graphs and Hypergraphs Hypergraphs (, ) are

Hypergraphs in Chaos JULIUS LISCHEID Graphs and Hypergraphs Hypergraphs (, ) are

Hypergraphs in Chaos JULIUS LISCHEID Graphs and Hypergraphs Hypergraphs (, ) are generalised graphs where hyperedges e E contain an arbitrary number of v 1 vertices v v 2 In short, E ()

385 views • 9 slides
Transversals and Trades in Latin Squares. Trent G. Marbach Monash University September 5, 2016

Transversals and Trades in Latin Squares. Trent G. Marbach Monash University September 5, 2016

Outline Introduction Transversals -way k -homogeneous latin trades Transversals and Trades in Latin Squares. Trent G. Marbach Monash University September 5, 2016 Transversals work with Ji Lijun - Suzhou University Trent G. Marbach

883 views • 67 slides
FPT algorithms for path-transversals and cycle-transversals problems in graphs S. Guillemot

FPT algorithms for path-transversals and cycle-transversals problems in graphs S. Guillemot

FPT algorithms for path-transversals and cycle-transversals problems in graphs S. Guillemot INRIA, France 20 February 2008 S. Guillemot (INRIA, France) FPT algorithms ... 20 February 2008 1 / 10 Introduction In short: We consider graph

446 views • 23 slides
Lagrangians of Hypergraphs Peng, Yuejian Hunan University November 09, 2013 Lagrangians of

Lagrangians of Hypergraphs Peng, Yuejian Hunan University November 09, 2013 Lagrangians of

Lagrangians of Hypergraphs Lagrangians of Hypergraphs Peng, Yuejian Hunan University November 09, 2013 Lagrangians of Hypergraphs Outline Applications of Lagrangians in Tur an type problem 1 Extension of Motzkin-Straus Theorem to some

532 views • 36 slides
Generalised transversals of Latin squares Ian Wanless Monash University [EJC1] I. M. Wanless, A

Generalised transversals of Latin squares Ian Wanless Monash University [EJC1] I. M. Wanless, A

Generalised transversals of Latin squares Ian Wanless Monash University [EJC1] I. M. Wanless, A generalisation of transversals for Latin squares, Electron. J. Combin. , 9(1) (2002), #R12. [EJC2] N. J. Cavenagh and I. M. Wanless, Latin squares

838 views • 42 slides
Further Consequences of the Colorful Helly Hypothesis: Beyond Point Transversals Leonardo I.

Further Consequences of the Colorful Helly Hypothesis: Beyond Point Transversals Leonardo I.

Further Consequences of the Colorful Helly Hypothesis: Beyond Point Transversals Leonardo I. Mart nez Sandoval (Ben-Gurion University) Joint work with Edgardo Rold an Pensado (UNAM) and Natan Rubin (BGU) ERC Workshop, Ein Gedi March

968 views • 55 slides
On the Cycle Structures of Hypergraphs Jianfang Wang Academy of Mathematics and System Science,

On the Cycle Structures of Hypergraphs Jianfang Wang Academy of Mathematics and System Science,

On the Cycle Structures of Hypergraphs On the Cycle Structures of Hypergraphs Jianfang Wang Academy of Mathematics and System Science, Chinese Academy of Science. Beijing 100190, China. 1 / 23 On the Cycle Structures of Hypergraphs 1. Cycle

694 views • 23 slides
Acyclicity, Simple Connectivity and Covers of Hypergraphs Julian Bitterlich

Acyclicity, Simple Connectivity and Covers of Hypergraphs Julian Bitterlich

Motivation and Proviso Graphs Hypergraphs Final result/Summary Acyclicity, Simple Connectivity and Covers of Hypergraphs Julian Bitterlich bitterlich@mathematik.tu-darmstadt.de Fachbereich Mathematik TU-Darmstadt May 4, 2017 Motivation

543 views • 19 slides
Universal centralizers and Poisson transversals Ana B alibanu Harvard University Friday Fish

Universal centralizers and Poisson transversals Ana B alibanu Harvard University Friday Fish

Universal centralizers and Poisson transversals Ana B alibanu Harvard University Friday Fish Online September 11, 2020 1 The universal centralizer G semisimple algebraic group of adjoint type over C rank p G q l g Lie G The

323 views • 20 slides
IMDAD ULLAH KHAN UMM AL-QURA UNIVERSITY June 12, 2013 Hypergraphs A hypergraph H is a family of

IMDAD ULLAH KHAN UMM AL-QURA UNIVERSITY June 12, 2013 Hypergraphs A hypergraph H is a family of

PERFECT MATCHINGS IN UNIFORM HYPERGRAPHS IMDAD ULLAH KHAN UMM AL-QURA UNIVERSITY June 12, 2013 Hypergraphs A hypergraph H is a family of subsets ( E ( H )) of a ground set V ( H ) H = ( V , E ) | V ( H ) | = n 1 2 3 6 H := E 5 4 V = { 1 ,

481 views • 32 slides
Eulerian-type properties of hypergraphs Mateja Sajna University of Ottawa Joint

Eulerian-type properties of hypergraphs Mateja Sajna University of Ottawa Joint

Eulerian-type properties of hypergraphs Mateja Sajna University of Ottawa Joint work with Amin Bahmanian CanaDAM 2013 Mateja Sajna (U of Ottawa) Eulerian hypergraphs 1 / 29 Outline Basic definitions. Walks, trails,

556 views • 29 slides
Math in the Real World Mrs. Cecil Period 1-2 LT1: Parallel Lines and Transversals Andrew

Math in the Real World Mrs. Cecil Period 1-2 LT1: Parallel Lines and Transversals Andrew

Math in the Real World Mrs. Cecil Period 1-2 LT1: Parallel Lines and Transversals Andrew is making a toothpick bridge for his science project. He is modeling his bridge after the one shown in the picture. Find m 2 if m 1 = 40

448 views • 12 slides
Coloring Simple Hypergraphs Dhruv Mubayi Department of Mathematics, Statistics and Computer

Coloring Simple Hypergraphs Dhruv Mubayi Department of Mathematics, Statistics and Computer

Coloring Simple Hypergraphs Dhruv Mubayi Department of Mathematics, Statistics and Computer Science University of Illinois Chicago May 13, 2011 Dhruv Mubayi Coloring Simple Hypergraphs A Puzzle Problem Let n 2 and suppose that S [ n

1.37k views • 103 slides
Counting minimal transversals in -acyclic Hypergraph Benjamin Bergougnoux, Florent Capelli ,

Counting minimal transversals in -acyclic Hypergraph Benjamin Bergougnoux, Florent Capelli ,

Counting minimal transversals in -acyclic Hypergraph Benjamin Bergougnoux, Florent Capelli , Mamadou M. Kant LIMOS, CNRS, Universit Clermont Auvergne Universit Lille 3, CRIStAL, CNRS, INRIA Algorithm Seminar, Bergen,

621 views • 43 slides
Transversal Theory and Reverse Mathematics Noah A. Hughes hughesna @ appstate.edu Appalachian

Transversal Theory and Reverse Mathematics Noah A. Hughes hughesna @ appstate.edu Appalachian

Transversal Theory and Reverse Mathematics Noah A. Hughes hughesna @ appstate.edu Appalachian State University Boone, NC Thursday, April 3, 2014 National Conference on Undergraduate Research University of Kentucky Transversals Transversals

583 views • 25 slides
Click to edit Master title style Skeleton computation of an image using a geometric approach J.

Click to edit Master title style Skeleton computation of an image using a geometric approach J.

Click to edit Master title style Skeleton computation of an image using a geometric approach J. Martinez, M. Vigo, N. Pla-Garcia, D. Ayala Introduction One of the challenges of BioCAD field is to understand the morphology of the pore

412 views • 29 slides
Recentered Influence Functions (RIF) in Stata RIF-regression and RIF-decomposition Fernando

Recentered Influence Functions (RIF) in Stata RIF-regression and RIF-decomposition Fernando

Recentered Influence Functions (RIF) in Stata RIF-regression and RIF-decomposition Fernando Rios-Avila 1 1 Levy Economics Institute Bard College Stata Conference-Chicago 2019 Rios-Avila (Levy) RIF Stata Chicago 2019 1 / 47 Table of Contents

475 views • 47 slides
Poster #46 How Much Restricted Isometry is Needed in Nonconvex Matrix Recovery? Richard Y.

Poster #46 How Much Restricted Isometry is Needed in Nonconvex Matrix Recovery? Richard Y.

Wed Dec 5th 5 - 7 PM @ Room 210 & 230 AB Neural Information Processing Systems 2018 Poster #46 How Much Restricted Isometry is Needed in Nonconvex Matrix Recovery? Richard Y. Cdric Javad Somayeh Zhang Josz Sojoudi Lavaei 1

408 views • 37 slides
Computational Geometry Part 1: Intro, Primitives, Area, Circles Lucca Siaudzionis and Jack

Computational Geometry Part 1: Intro, Primitives, Area, Circles Lucca Siaudzionis and Jack

Computational Geometry Part 1: Intro, Primitives, Area, Circles Lucca Siaudzionis and Jack Spalding-Jamieson 2020/02/25 University of British Columbia Announcements A3 is due Sunday! Project topics are due next Tuesday! 1 What is

431 views • 40 slides
Measuring the Dark Force at the LHC Zhenyu Han UC Davis Reference: arXiv 0902.0006 (with Yang

Measuring the Dark Force at the LHC Zhenyu Han UC Davis Reference: arXiv 0902.0006 (with Yang

Measuring the Dark Force at the LHC Zhenyu Han UC Davis Reference: arXiv 0902.0006 (with Yang Bai @ Fermilab) 05/12/2009 @ PHENO 09 Outline Motivation Positron/electron excesses in cosmic rays, PAMELA, ATIC, FERMI... A class of

430 views • 19 slides
P s rt r r

P s rt r r

P s rt r r strts t r t srs r

2.21k views • 186 slides
Hard Lefschetz theorem and Hodge-Riemann relations for combinatorial geometries June Huh

Hard Lefschetz theorem and Hodge-Riemann relations for combinatorial geometries June Huh

Hard Lefschetz theorem and Hodge-Riemann relations for combinatorial geometries June Huh Institute for Advanced Study and Princeton University with Karim Adiprasito and Eric Katz June Huh 1 / 26 A graph is a -dimensional space, with

576 views • 46 slides
Conjugate Phase Retrieval in the Paley-Wiener Space Eric Weber Iowa State University CodEx

Conjugate Phase Retrieval in the Paley-Wiener Space Eric Weber Iowa State University CodEx

Conjugate Phase Retrieval in the Paley-Wiener Space Eric Weber Iowa State University CodEx Seminar September 22, 2020 Eric Weber Conjugate Phase Retrieval in the Paley-Wiener Space 1 / 26 Acknowledgements ChunKit Lai Friedrich Littmann

388 views • 26 slides

More recommend