IC-planar graphs are odd-10-colorable

Chenran Pan, Weifan Wang and Runrun Liu

Applied Mathematics and Computation, 2023, vol. 451, issue C

Abstract: An odd-k-coloring of a graph G is a proper k-coloring such that for every vertex v∈V(G) with d(v)≥1, there exists a color occurring odd times in its neighbors. The odd chromatic number, denote by χo(G), of G is the smallest integer k so that G admits an odd-k-coloring. Call a graph G IC-planar if it can be drawn in the plane so that every edge is crossed by at most once and every vertex has at most one incident edge being crossed. It was shown that every planar graph G has χo(G)≤8. In this paper we show that every IC-planar graph G satisfies χo(G)≤10.

Keywords: IC-planar graph; Discharging; Odd coloring; Reducible configuration (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:451:y:2023:i:c:s0096300323001893

DOI: 10.1016/j.amc.2023.128020

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