2-Distance coloring of planar graphs without triangles and intersecting 4-cycles

Abstract

The k-2-distance coloring of graph G is a mapping [Formula: see text] if any two vertices at distance at most two from each other get different colors. The 2-distance chromatic number is the smallest integer k such that G has a k-2-distance coloring, denoted by [Formula: see text]. In this paper, we prove that every planar graph G without 3-cycles and intersecting 4-cycles and [Formula: see text] has [Formula: see text].