The half-monochromatic colorings of plane graphs with even polygonal faces

TL;DR

This paper introduces half-monochromatic colorings for plane graphs with even polygonal faces, providing an upper bound on the maximum number of colors based on the independence number, extending previous work on anti-rainbow colorings.

Contribution

It extends the concept of anti-rainbow colorings to half-monochromatic colorings in plane graphs with even faces, establishing an upper bound related to the independence number.

Findings

Derived an upper bound for half-monochromatic colorings.

Extended previous bounds from anti-rainbow to half-monochromatic colorings.

Applicable to plane graphs with even polygonal faces.

Abstract

On the maximum number of colors for proper anti-rainbow colorings on a planar quadrangulation, an upper bound was given by Enami-Ozeki-Yamaguchi in terms of the 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.