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 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.