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SUMMARY:Cycle-complete Ramsey numbers - Peter Keevash (University of Oxfor
 d)
DTSTART:20190207T143000Z
DTEND:20190207T153000Z
UID:TALK117040@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:The cycle-complete Ramsey number f(k\,n) is the smallest numbe
 r N such that any red/blue edge-colouring of K_N contains a red C_k (k-cyc
 le) or a blue K_n (complete graph on n vertices). In 1978\, Erdos\, Faudre
 e\, 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 multiplicativ
 e constants. This is joint work with Eoin\nLong and Jozef Skokan.\n
LOCATION:MR12
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