On the Multi-Colored Ramsey Numbers of Paths and Even Cycles

  • Gábor N. Sárközy
Keywords: Ramsey numbers, Paths, Cycles

Abstract

In this paper we improve the upper bound on the multi-color Ramsey numbers of paths and even cycles. More precisely, we prove the following. For every r2 there exists an n0=n0(r) such that for nn0 we have Rr(Pn)(rr16r3+1)n. For every r2 and even n we have Rr(Cn)(rr16r3+1)n+o(n) as n. The main tool is a stability version of the Erdős-Gallai theorem that may be of independent interest.

Published
2016-09-30
Article Number
P3.53