An improved bound on 2-distance coloring plane graphs with girth 5

摘要

A vertex coloring is called -distance if any two vertices at distance at most from each other get different colors. The minimum number of colors in 2-distance colorings of is its 2-distance chromatic number, denoted by . Let be a plane graph with girth at least . In this paper, we prove that for arbitrary , which partially improves some known results.