Some results on 2-distance coloring of planar graphs with girth five

Zakir Deniz ()
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Zakir Deniz: Düzce University

Journal of Combinatorial Optimization, 2024, vol. 47, issue 4, No 15, 25 pages

Abstract: 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. Suppose that G is a planar graph with girth 5 and maximum degree $$\Delta $$ Δ . We prove that G admits a 2-distance $$\Delta +7$$ Δ + 7 coloring, which improves the result of Dong and Lin (J Comb Optim 32(2):645–655, 2016). Moreover, we prove that G admits a 2-distance $$\Delta +6$$ Δ + 6 coloring when $$\Delta \ge 10$$ Δ ≥ 10 .

Keywords: Coloring; 2-distance coloring; Girth; Planar graph (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10878-024-01169-z

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