An improvement of the 2-distance chromatic number of planar graphs with maximum degree at most 6
Sara Al Hajjar
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Source: Crossref
Published: Sep 7, 2026
DOI: 10.1142/s1793830926500801
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A 2-distance [Formula: see text]-coloring of a graph is a proper coloring of the vertices of the graph using [Formula: see text] colors such that any two vertices at distance two or less get distinct colors. The 2-distance chromatic number of a graph [Formula: see text], denoted as [Formula: see text], is the minimum integer [Formula: see text] such that [Formula: see text] admits a 2-distance [Formula: see text]-coloring. In [Improved square coloring of planar graphs, Discrete Math. 346(4) (2023) 113288], Bousquet et al. proved that [Formula: see text] for planar graphs with maximum degree [Formula: see text] For a planar graph [Formula: see text] with a maximum degree [Formula: see text] at most 6, we prove that [Formula: see text] hence improving the bound of [Formula: see text] for planar graphs with [Formula: see text].
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