On 2-Distance ($\Delta +4$)-coloring of planar graphs with girth at least five

Abstract

A vertex coloring of a graph $G$ is called a 2-distance coloring if any two vertices at distance at most $2$ from each other receive different colors. Let $G$ be a planar graph with girth at least $5$. We prove that $G$ admits a $2$-distance coloring with $\Delta +4$ colors if $\Delta \ge 22$.

10 pages. arXiv admin note: text overlap with arXiv:2308.00390