Acyclic 3-coloring of generalized Petersen graphs

Enqiang Zhu (), Zepeng Li, Zehui Shao, Jin Xu and Chanjuan Liu
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Enqiang Zhu: Peking University
Zepeng Li: Peking University
Zehui Shao: Chengdu University
Jin Xu: Peking University
Chanjuan Liu: Peking University

Journal of Combinatorial Optimization, 2016, vol. 31, issue 2, No 29, 902-911

Abstract: Abstract An acyclic $$k$$ k -coloring of a graph $$G$$ G is a $$k$$ k -coloring of its vertices such that no cycle of $$G$$ G is bichromatic. $$G$$ G is called acyclically $$k$$ k -colorable if it admits an acyclic $$k$$ k -coloring. In this paper, we prove that the generalized Petersen graph $$P(n,k)$$ P ( n , k ) is acyclically 3-colorable except $$P(4,1)$$ P ( 4 , 1 ) and the classical Petersen graph $$P(5,2)$$ P ( 5 , 2 ) .

Keywords: Acyclic coloring; Generalized Petersen graphs; Cubic graphs; Triconnectivity (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-014-9799-9

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