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Integral Unit Bar-Visibility Graphs Therese Biedl Ahmad Biniaz - PowerPoint PPT Presentation

Apr 11, 2023 •104 likes •1.75k views

Integral Unit Bar-Visibility Graphs Therese Biedl Ahmad Biniaz Veronika Irvine Philipp Kindermann Anurag Murty Naredla Alexi Turcotte Integral Unit Bar-Visibility Integral Unit Bar-Visibility Integral Unit Bar-Visibility Integral Unit

  1. Integral Unit Bar-Visibility Graphs Therese Biedl Ahmad Biniaz Veronika Irvine Philipp Kindermann Anurag Murty Naredla Alexi Turcotte

  2. Integral Unit Bar-Visibility

  3. Integral Unit Bar-Visibility

  4. Integral Unit Bar-Visibility

  5. Integral Unit Bar-Visibility

  6. Integral Unit Bar-Visibility

  7. Integral Unit Bar-Visibility

  8. Integral Unit Bar-Visibility Strong ⇔

  9. Integral Unit Bar-Visibility Weak Strong ⇒ ⇔

  10. Integral Unit Bar-Visibility Weak Strong ⇒ ⇔

  11. Integral Unit Bar-Visibility Every planar graph, O ( n ) time Weak Strong ⇒ ⇔

  12. Integral Unit Bar-Visibility 3-connected: NP-hard Every planar graph, O ( n ) time Weak Strong ⇒ ⇔

  13. Integral Unit Bar-Visibility 3-connected: NP-hard Triangulation: O ( n ) time Every planar graph, O ( n ) time Weak Strong ⇒ ⇔

  14. Integral Unit Bar-Visibility 3-connected: NP-hard Triangulation: O ( n ) time Every planar graph, 4-connected: O ( n ) time O ( n ) time Weak Strong ⇒ ⇔

  15. Integral Unit Bar-Visibility Weak Strong ⇒ ⇔

  16. Integral Unit Bar-Visibility Weak Strong ⇒ ⇔

  17. Integral Unit Bar-Visibility Characterizations for... Weak Strong ⇒ ⇔

  18. Integral Unit Bar-Visibility Characterizations for... • trees Weak Strong ⇒ ⇔

  19. Integral Unit Bar-Visibility Characterizations for... • trees • complete bipartite Weak Strong ⇒ ⇔

  20. Integral Unit Bar-Visibility Characterizations for... • trees • complete bipartite • outerplanar Weak Strong ⇒ ⇔

  21. Integral Unit Bar-Visibility Characterizations for... • trees • complete bipartite • outerplanar • triangulations Weak Strong ⇒ ⇔

  22. Integral Unit Bar-Visibility Weak Strong ⇒ ⇔

  23. Integral Unit Bar-Visibility 0 1 2 3 4 5 6 7 8 Weak Strong ⇒ ⇔

  24. Integral Unit Bar-Visibility 0 1 2 3 4 5 6 7 8 Weak Strong ⇒ ⇔

  25. Integral Unit Bar-Visibility 0 1 2 3 4 5 6 7 8 Weak Strong ⇒ ⇔

  26. Integral Unit Bar-Visibility 0 1 2 3 4 5 6 7 8 Weak Strong ⇒ ⇔

  27. Integral Unit Bar-Visibility 0 1 2 3 4 5 6 7 8 Weak Strong ⇒ ⇔

  28. Integral Unit Bar-Visibility 0 1 2 3 4 5 6 7 8 Weak Strong ⇒ ⇔

  29. Integral Unit Bar-Visibility 0 1 2 3 4 5 6 7 8 Weak Strong ⇒ ⇔

  30. Integral Unit Bar-Visibility 0 1 2 3 4 5 6 7 8 Weak Strong ⇒ ⇔

  31. Integral Unit Bar-Visibility max-deg 6 0 1 2 3 4 5 6 7 8 Weak Strong ⇒ ⇔

  32. Weak Model ⇒

  33. Weak: Trees, maxdeg 5 v

  34. Weak: Trees, maxdeg 5 v v

  35. Weak: Trees, maxdeg 5 v v

  36. Weak: Trees, maxdeg 5 v v

  37. Weak: Trees, maxdeg 5 v v

  38. Weak: Trees, maxdeg 5 v v

  39. Weak: Trees, maxdeg 5 v v

  40. Weak: Trees, maxdeg 5 v v

  41. Weak: Trees, maxdeg 5 v v

  42. Weak: Trees, maxdeg 5 v v Tree with maxdeg 5 ✗

  43. Weak: Trees, maxdeg 4

  44. Weak: Trees, maxdeg 4

  45. Weak: Trees, maxdeg 4

  46. Weak: Trees, maxdeg 4

  47. Weak: Trees, maxdeg 4

  48. Weak: Trees, maxdeg 4 Tree with maxdeg 4 ✓

  49. Weak: Biconnected Outerplanar, maxdeg 3

  50. Weak: Biconnected Outerplanar, maxdeg 3

  51. Weak: Biconnected Outerplanar, maxdeg 3

  52. Weak: Biconnected Outerplanar, maxdeg 3

  53. Weak: Biconnected Outerplanar, maxdeg 3

  54. Weak: Biconnected Outerplanar, maxdeg 3

  55. Weak: Biconnected Outerplanar, maxdeg 3

  56. Weak: Biconnected Outerplanar, maxdeg 3

  57. Weak: Biconnected Outerplanar, maxdeg 3

  58. Weak: Biconnected Outerplanar, maxdeg 3

  59. Weak: Biconnected Outerplanar, maxdeg 3

  60. Weak: Biconnected Outerplanar, maxdeg 3

  61. Weak: Biconnected Outerplanar, maxdeg 3

  62. Weak: Biconnected Outerplanar, maxdeg 3

  63. Weak: Biconnected Outerplanar, maxdeg 3

  64. Weak: Biconnected Outerplanar, maxdeg 3 Biconnected Outerplanar ✓ with maxdeg 3

  65. Weak: Biconnected Outerplanar, maxdeg 4

  66. Weak: Biconnected Outerplanar, maxdeg 4

  67. Weak: Biconnected Outerplanar, maxdeg 4

  68. Weak: Biconnected Outerplanar, maxdeg 4

  69. Weak: Biconnected Outerplanar, maxdeg 4

  70. Weak: Biconnected Outerplanar, maxdeg 4

  71. Weak: Biconnected Outerplanar, maxdeg 4

  72. Weak: Biconnected Outerplanar, maxdeg 4

  73. Weak: Biconnected Outerplanar, maxdeg 4

  74. Weak: Biconnected Outerplanar, maxdeg 4

  75. Weak: Biconnected Outerplanar, maxdeg 4 Biconnected Outerplanar ✓ with maxdeg 4

  76. Weak: Biconnected Outerplanar, maxdeg 4

  77. Weak: Biconnected Outerplanar, maxdeg 4

  78. Weak: Biconnected Outerplanar, maxdeg 4

  79. Weak: Biconnected Outerplanar, maxdeg 4

  80. Weak: Biconnected Outerplanar, maxdeg 4

  81. Layered Drawings

  82. Layered Drawings

  83. Layered Drawings

  84. Layered Drawings

  85. Layered Drawings consecutive consecutive

  86. Weak: NP-hardness

  87. Weak: NP-hardness

  88. Weak: NP-hardness NP-hard [Heath & Rosenberg]

  89. Weak: NP-hardness NP-hard [Heath & Rosenberg]

  90. Weak: NP-hardness NP-hard [Heath & Rosenberg] P

  91. Weak: NP-hardness Edges:

  92. Weak: NP-hardness Edges:

  93. Weak: NP-hardness Edges: Node block:

  94. Weak: NP-hardness Edges: Node block:

  95. Weak: NP-hardness Edges: Node block:

  96. Weak: NP-hardness Edges: Node block:

  97. Weak: NP-hardness Edges: Node block:

  98. Weak: NP-hardness Edges: Node block:

  99. Weak: NP-hardness Edges: Node block:

  100. Weak: NP-hardness Edges: Node block: Nodes:

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