Multicolour Ramsey Numbers of Odd Cycles

2016/02/24 by Day, A. Nicholas, Johnson, J. Robert · 3 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1602.07607

Abstract

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.

Cited by

• An improved upper bound for the multicolour Ramsey number of odd cycles
• Short monochromatic odd cycles
• New upper bound for the Ramsey number of odd cycles

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