2-Distance coloring of planar graphs with girth 5

Wei Dong () and Baogang Xu ()
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Wei Dong: Nanjing XiaoZhuang University
Baogang Xu: Nanjing Normal University

Journal of Combinatorial Optimization, 2017, vol. 34, issue 4, No 18, 1302-1322

Abstract: Abstract A vertex coloring is said to be 2-distance if any two distinct vertices of distance at most 2 receive different colors. Let G be a planar graph with girth at least 5. In this paper, we prove that G admits a 2-distance coloring with at most $$\Delta (G)+3$$ Δ ( G ) + 3 colors if $$\Delta (G)\ge 339$$ Δ ( G ) ≥ 339 .

Keywords: Girth; Planar graph; 2-Distance coloring; 05C15; 05C78 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-017-0148-7

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