Multicolour Ramsey Numbers of Odd Cycles

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• Nick Day (QMUL)
• Thursday 16 June 2016, 14:30-15:30
• MR12.

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

We show that for any positive integer r there exists an integer k and a k-colouring of the complete graph of order 2^{k+ 1} such that the colouring contains no monochromatic odd cycle of length less than 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 and prove that, for all odd r and all k sufficiently large, there exists a constant c = c® > 0 such that the k-colour Ramsey number of the r-cycle is at least (r-1)(2+c)^k-1.

This is joint work with Robert Johnson.

This talk is part of the Combinatorics Seminar series.

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