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SUMMARY:Joseph Hyde (Warwick)
DTSTART:20211103T140000Z
DTEND:20211103T150000Z
DTSTAMP:20260423T003234Z
UID:WCS/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WCS/40/">Pro
 gress on the Kohayakawa-Kreuter conjecture</a>\nby Joseph Hyde (Warwick) a
 s part of Warwick Combinatorics Seminar\n\n\nAbstract\nLet $H_1\, ...\, H_
 r$ be graphs. We write $G(n\,p) \\to (H_1\, ...\, H_r)$ to denote the prop
 erty that whenever we colour the edges of $G(n\,p)$ with colours from the 
 set $[r] := \\{1\, ...\, r\\}$ there exists some $1 \\le i \\le r$ and a c
 opy of $H_i$ in $G(n\,p)$ monochromatic in colour $i$.\n\nThere has been m
 uch interest in determining the asymptotic threshold function for this pro
 perty. Rödl and Ruciński (1995) determined the threshold function for th
 e general symmetric case\; that is\, when $H_1 = ... = H_r$. A conjecture 
 of Kohayakawa and Kreuter (1997)\, if true\, would effectively resolve the
  asymmetric problem. Recently\, the $1$-statement of this conjecture was c
 onfirmed by Mousset\, Nenadov and Samotij (2021+). The $0$-statement howev
 er has only been proved for pairs of cycles\, pairs of cliques and pairs o
 f a clique and a cycle.\n\nIn this talk we introduce a reduction of the $0
 $-statement of Kohayakawa and Kreuter's conjecture to a certain determinis
 tic\, natural subproblem. To demonstrate the potential of this approach\, 
 we show this subproblem can be resolved for almost all pairs of regular gr
 aphs (satisfying properties one can assume when proving the $0$-statement)
 .\n
LOCATION:https://researchseminars.org/talk/WCS/40/
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