A note on (t - 1)-chromatic Ramsey number of linear forests

Abstract

Given t distinct colors, we order the t subsets of t−1 colors in some arbitrary manner. Let $G_1,G_2,\dots ,G_t$ be graphs. The $(t-1)$-chromatic Ramsey number, denoted by $r_{t-1}^t(G_1,G_2,\dots ,G_t)$, is defined to be the least number n such that if the edges of the complete graph $K_n$ are colored in any fashion with t colors, then for some i the subgraph whose edges are colored with the ith subset of colors contains a $G_i$. In this paper, we study the $(t-1)$-chromatic Ramsey number of linear forests.

Keywords:

• Ramsey numbers
• $(t-1)$-chromatic Ramsey numbers
• edge coloring

2010 Mathematics Subject Classifications:

• 05C55
• 05D10

Acknowledgments

The author would like to thank the anonymous referee for several valuable comments and suggestions which significantly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Amir Khamseh  http://orcid.org/0000-0001-5077-634X

Additional information

Funding

This research was in part supported by a grant from School of Mathematics, Institute for Research in Fundamental Sciences (IPM) (No. 94030059).