Abstract
Given t distinct colors, we order the t subsets of t−1 colors in some arbitrary manner. Let be graphs. The
-chromatic Ramsey number, denoted by
, is defined to be the least number n such that if the edges of the complete graph
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
. In this paper, we study the
-chromatic Ramsey number of linear forests.
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