Equitable colorings of Cartesian products of square of cycles and paths with complete bipartite graphs

摘要

A graph G is said to be equitably k-colorable if the vertex set of G can be divided into k independent sets for which any two sets differ in size at most one. The equitable chromatic number of G, , is the minimum k for which G is equitably k-colorable. The equitable chromatic threshold of G, , is the minimum k for which G is equitably -colorable for all . In this paper, the exact values of and are obtained when G is the square of a cycle or a path and H is a complete bipartite graph.