University of Birmingham > Talks@bham > Combinatorics and Probability seminar > Progress on the Kohayakawa-Kreuter conjecture

Progress on the Kohayakawa-Kreuter conjecture

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If you have a question about this talk, please contact Johannes Carmesin.

Let H_1, ..., H_r be graphs. We write G(n,p) → (H_1, ..., H_r) to denote the property that whenever we colour the edges of G(n,p) with colours from the set {1, ..., r} there exists some 1 ≤ i ≤ r and a copy of H_i in G(n,p) monochromatic in colour i.

There has been much interest in determining the asymptotic threshold function for this property. Rödl and Ruciński (1995) determined the threshold function for the general symmetric case; that is, when H_1 = ... = H_r. A conjecture of Kohayakawa and Kreuter (1997), if true, would fully resolve the asymmetric problem. Recently, the 1-statement of this conjecture was confirmed by Mousset, Nenadov and Samotij (2021+). The 0-statement however has only been proved for pairs of cycles, pairs of cliques and pairs of a clique and a cycle.

This talk is part of the Combinatorics and Probability seminar series.

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