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SUMMARY:Multicolour Ramsey Numbers of Odd Cycles - Nick Day (QMUL)
DTSTART:20160616T133000Z
DTEND:20160616T143000Z
UID:TALK65532@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:We show that for any positive integer r there exists an intege
 r k and a k-colouring of the complete graph of order 2<sup>k+ 1</sup> such
  that the colouring contains no monochromatic odd cycle of length less tha
 n r. This answers a question of Erdős and Graham. We use these colourings
  to give new lower bounds on the k-colour Ramsey number of the odd cycle a
 nd prove that\, for\nall odd r and all k sufficiently large\, there exists
  a constant c = c(r) > 0 such that the k-colour Ramsey number of the r-cyc
 le is at least (r-1)(2+c)<sup>k-1</sup>.\n\nThis is joint work with Robert
  Johnson.
LOCATION:MR12
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