Acyclic coloring of graphs with some girth restriction

Jiansheng Cai (), Binlu Feng and Guiying Yan
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Jiansheng Cai: Weifang University
Binlu Feng: Weifang University
Guiying Yan: Chinese Academy of Science

Journal of Combinatorial Optimization, 2016, vol. 31, issue 4, No 3, 1399-1404

Abstract: Abstract A vertex coloring of a graph $$G$$ G is called acyclic if it is a proper vertex coloring such that every cycle $$C$$ C receives at least three colors. The acyclic chromatic number of $$G$$ G is the least number of colors in an acyclic coloring of $$G$$ G . We prove that acyclic chromatic number of any graph $$G$$ G with maximum degree $$\Delta \ge 4$$ Δ ≥ 4 and with girth at least $$4\Delta $$ 4 Δ is at most $$12\Delta $$ 12 Δ .

Keywords: Graph; Girth; Coloring; Acyclic coloring; Local lemma (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-015-9829-2

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