An Improved Bound on the Chromatic Number of the Pancake Graphs

In this paper, an improved bound on the chromatic number of the Pancake graph P-n, n > 9, is presented. The bound is obtained using a subadditivity property of the chromatic number of the Pancake graph. We also investigate an equitable coloring of P-n. An equitable (n - 1)-coloring based on efficient dominating sets is given and optimal equitable 4-colorings are considered for small n. It is conjectured that the chromatic number of P-n coincides with its equitable chromatic number for any n > 2.