Multicolour Ramsey Numbers of Odd Cycles [article]

A. Nicholas Day, J. Robert Johnson
2017 arXiv   pre-print
We show that for any positive integer r there exists an integer k and a k-colouring of the edges of K_2^k+1 with no monochromatic odd cycle of length less than r. This makes progress on a problem of Erdős and Graham and answers a question of Chung. 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 ϵ = ϵ(r) > 0 such that R_k(C_r) > (r-1)(2+ϵ)^k-1.
arXiv:1602.07607v2 fatcat:wo6oectounhxtctedfqv2tzzqu