The Half-Monochromatic Colorings of Plane Graphs with Even Polygonal Faces

Abstract

An upper bound was given by Enami–Ozeki–Yamaguchi on the maximum number of colors for proper anti-rainbow colorings on a planar quadrangulation in terms of its independence number. In this paper, as an extension, we introduce the half-monochromatic coloring on a plane graph with even polygonal faces, and give an upper bound on the maximum number of colors for such colorings in terms of the independence number.