An Improvement of the Bound on the Odd Chromatic Number of 1-Planar Graphs

Abstract

AbstractAn odd coloring of a graph is a proper coloring in such a way that every non-isolated vertex has some color that appears an odd number of times on its neighborhood. A graph is 1-planar if it has a drawing in the plane so that each edge is crossed at most once. Cranston, Lafferty, and Song showed that every 1-planar graph admits an odd 23-coloring [arXiv:2202.02586v4]. In this paper, we improve their bound to 16.Keywords1-planar graphOdd coloringDischarging