On the multi-colored ramsey numbers of paths and even cycles

Sárközy, Gábor (2016) On the multi-colored ramsey numbers of paths and even cycles. ELECTRONIC JOURNAL OF COMBINATORICS, 23 (3). pp. 1-10. ISSN 1097-1440

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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 r ≥ 2 there exists an n0 = n0(r) such that for n ≥ n0 we have (Formula Presented). For every r ≥ 2 and even n we have (Formula Presented). The main tool is a stability version of the Erdős-Gallai theorem that may be of independent interest. © 2016 Australian National University. All rights reserved.

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