Abstract
Chung and Liu have defined the d‐chromatic Ramsey number as follows. Let 1 ≤ d ≤ c and let . Let 1, 2, …, t be the ordered subsets of d colors chosen from c distinct colors. Let G1, G2, …, Gt be graphs. The d‐chromatic Ramsey number denoted by is defined as the least number p such that, if the edges of the complete graph Kp are colored in any fashion with c colors, then for some i, the subgraph whose edges are colored in the ith subset of colors contains a Gi. In this paper it is shown that where i ≤ j ≤ k < r(Pi, Pj), stands for a generalized Ramsey number on a 2‐colored graph and Pi is a path of order i.
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More From: International Journal of Mathematics and Mathematical Sciences
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