Improved 2-distance coloring of planar graphs with maximum degree 5

A 2-distance k-coloring of a graph G is a proper k-coloring such that any two vertices at distance two or less get different colors. The 2-distance chromatic number of G is the minimum k such that G has a 2-distance k-coloring, denoted by chi 2(G). 2 ( G ). In this paper, we show that chi 2(G) 2 ( G ) <= 17 for every planar graph G with maximum degree A(G) G ) <= 5, which improves a former bound chi 2(G) 2 ( G ) <= 18. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.