List 2-distance coloring of planar graphs

Yuehua Bu () and Xiaoyan Yan
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Yuehua Bu: Zhejiang Normal University
Xiaoyan Yan: Zhejiang Normal University

Journal of Combinatorial Optimization, 2015, vol. 30, issue 4, No 23, 1180-1195

Abstract: Abstract The $$2$$ 2 -distance coloring of a graph $$G$$ G is to color the vertices of $$G$$ G so that every two vertices at distance at most $$2$$ 2 from each other get different colors. Let $$\chi _{2}^{l}(G)$$ χ 2 l ( G ) be the list 2-distance chromatic number of $$G$$ G . In this paper, we show that (1) a planar graph $$G$$ G with $$\Delta (G)\ge 12$$ Δ ( G ) ≥ 12 which contains no $$3,5$$ 3 , 5 -cycles and intersecting 4-cycles has $$\chi _{2}^{l}(G)\le \Delta +6$$ χ 2 l ( G ) ≤ Δ + 6 ; (2) a planar graph $$G$$ G with $$\Delta (G)\le 5$$ Δ ( G ) ≤ 5 and $$g(G)\ge 5$$ g ( G ) ≥ 5 has $$\chi _{2}^{l}(G)\le 13$$ χ 2 l ( G ) ≤ 13 .

Keywords: Choice chromatic number; The maximum degree; 2-Distance coloring; Planar graphs (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10878-013-9700-2

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