2-Distance coloring of a planar graph without 3, 4, 7-cycles

Yuehua Bu () and Xia Lv
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Yuehua Bu: Zhejiang Normal University
Xia Lv: Zhejiang Normal University

Journal of Combinatorial Optimization, 2016, vol. 32, issue 1, No 15, 244-259

Abstract: Abstract A 2-distance coloring of a graph is a coloring of the vertices such that two vertices at distance at most two receive distinct colors. The 2-distance chromatic number $$\chi _{2}(G)$$ χ 2 ( G ) is the smallest k such that G is k-2-distance colorable. In this paper, we prove that every planar graph without 3, 4, 7-cycles and $$\Delta (G)\ge 15$$ Δ ( G ) ≥ 15 is ( $$\Delta (G)+4$$ Δ ( G ) + 4 )-2-distance colorable.

Keywords: 2-Distance coloring; Planar graph; Cycles (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-015-9873-y

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