Bipartite Polyhedral Maps on Closed Surfaces are Distinguishing 3-Colorable with Few Exceptions

Abstract

A map on a closed surface is said to be distinguishing k -colorable if it has a proper k-coloring such that no automorphism other than the identity map preserves the colors. We shall show that a polyhedral map with bipartite underlying graph is distinguishing 3-colorable if it has more than 18 vertices.