The Overlap Chromatic Numbers of Wheel Graphs

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.