Cycle-complete Ramsey numbers

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• Peter Keevash (University of Oxford)
• Thursday 07 February 2019, 14:30-15:30
• MR12.

If you have a question about this talk, please contact Andrew Thomason.

The cycle-complete Ramsey number f(k,n) is the smallest number N such that any red/blue edge-colouring of K_N contains a red C_k (k-cycle) or a blue K_n (complete graph on n vertices). In 1978, Erdos, Faudree, Rousseau and Schelp conjectured that f(k,n)=(k-1)(n-1)+1 if k>=n>=3 (except when k=n=3). I will describe a proof of this conjecture for large k. In fact, we show that f(k,n)=(k-1)(n-1)+1 whenever k is at least C log n / log log n, which is tight up to the value of the absolute constant C>0, and answers two further questions of Erdos et al. up to multiplicative constants. This is joint work with Eoin Long and Jozef Skokan.

This talk is part of the Combinatorics Seminar series.

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