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- W2035530079 abstract "Abstract We consider a conjecture by Kohayakawa, Łuczak, and Rödl, which, if true, would allow the application of Szemerédi's regularity lemma to show Turán‐type results for all random graphs and any fixed graph H . We deal with 5‐partite graphs such that each part contains n vertices, and any two parts form an ε‐regular pair with m edges. Here, two sets of vertices U and W of size n form an ε‐regular pair with m edges if all subsets U ′ ⊆ U and W ′ ⊆ W with | U ′|, | W ′| ≥ ε n satisfy || E ( U ′, W ′)| − | U ′| | W ′| m / n 2 | ≤ ε| U ′| | W ′| m / n 2 . We show that for each β > 0, there exists at most β m ( ) 10 such graphs that do not contain a K 5 as a subgraph if m ≥ Cn 5/3 for a constant C = C (β), ε is sufficiently small, and n is sufficiently large. This proves the special case of the conjecture when H equals the complete graph on five vertices. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004" @default.
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- W2035530079 date "2004-02-09" @default.
- W2035530079 modified "2023-10-15" @default.
- W2035530079 title "K5-free subgraphs of random graphs" @default.
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- W2035530079 doi "https://doi.org/10.1002/rsa.20000" @default.
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