The Overlap Chromatic Numbers of Wheel Graphs

Abstract

An $(r,\lambda )$ overlap coloring of a graph $G$ allocates $r$ colors to each vertex subject to the condition that any pair of adjacent vertices shares exactly $\lambda$ colors. The $(r,\lambda )$ overlap chromatic number of $G$ is the least number of colors required for such a coloring. The overlap chromatic numbers of bipartite graphs are easy to find; those of odd cycle graphs have already been established. In this paper, we find the overlap chromatic numbers of the wheel graphs.