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Jessica De Silva Department of Mathematics University of - - PowerPoint PPT Presentation
Jessica De Silva Department of Mathematics University of - - PowerPoint PPT Presentation
Increasing Paths Jessica De Silva Jessica De Silva Department of Mathematics University of Nebraska-Lincoln, USA SP Coding School 2015 Increasing Paths Jessica De Silva Increasing Paths Jessica De Silva Increasing Paths Jessica De Silva
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Increasing Paths Jessica De Silva
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Increasing Paths Jessica De Silva
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Increasing Paths Jessica De Silva
Increasing path of length 3.
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Increasing Paths Jessica De Silva
Fix a graph G.
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Increasing Paths Jessica De Silva
Fix a graph G. Let ϕ be an edge-ordering of G.
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Increasing Paths Jessica De Silva
Fix a graph G. Let ϕ be an edge-ordering of G. Define P(G, ϕ) to be the length of the longest increasing path in G with edge-ordering ϕ.
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Increasing Paths Jessica De Silva
Fix a graph G. Let ϕ be an edge-ordering of G. Define P(G, ϕ) to be the length of the longest increasing path in G with edge-ordering ϕ.
Goal is to find: f(G) := min
ϕ an edge-ordering P(G, ϕ)
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Increasing Paths Jessica De Silva
Theorem (Graham and Kleitman 1973)
1 2 √ 4n − 3 − 1
- ≤ f(Kn) ≤ 3
4n.
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Increasing Paths Jessica De Silva
Theorem (Graham and Kleitman 1973)
1 2 √ 4n − 3 − 1
- ≤ f(Kn) ≤ 3
4n.
Theorem (D., Molla, Pfender, Retter, Tait 2014+)
f(G(n, p)) ≥ (1 − o(1))√n with high probability whenever p ≥ ω(n) log n
√n and ω(n) → ∞
arbitrarily slowly.
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