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

Wei Dong () and Wensong Lin ()
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Wei Dong: Southeast University
Wensong Lin: Southeast University

Journal of Combinatorial Optimization, 2016, vol. 32, issue 2, No 19, 645-655

Abstract: Abstract A vertex coloring is called $$2$$ 2 -distance if any two vertices at distance at most $$2$$ 2 from each other get different colors. The minimum number of colors in 2-distance colorings of $$G$$ G is its 2-distance chromatic number, denoted by $$\chi _2(G)$$ χ 2 ( G ) . Let $$G$$ G be a plane graph with girth at least $$5$$ 5 . In this paper, we prove that $$\chi _2(G)\le \Delta +8$$ χ 2 ( G ) ≤ Δ + 8 for arbitrary $$\Delta (G)$$ Δ ( G ) , which partially improves some known results.

Keywords: Girth; Plane graph; 2-Distance coloring; 05C15; 05C78 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-015-9888-4

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