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Acyclic 3-coloring of generalized Petersen graphs

Author

Listed:
  • Enqiang Zhu

    (Peking University)

  • Zepeng Li

    (Peking University)

  • Zehui Shao

    (Chengdu University)

  • Jin Xu

    (Peking University)

  • Chanjuan Liu

    (Peking University)

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 ) .

Suggested Citation

  • Enqiang Zhu & Zepeng Li & Zehui Shao & Jin Xu & Chanjuan Liu, 2016. "Acyclic 3-coloring of generalized Petersen graphs," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 902-911, February.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:2:d:10.1007_s10878-014-9799-9
    DOI: 10.1007/s10878-014-9799-9
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    References listed on IDEAS

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    1. Patrizio Angelini & Fabrizio Frati, 2012. "Acyclically 3-colorable planar graphs," Journal of Combinatorial Optimization, Springer, vol. 24(2), pages 116-130, August.
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    Cited by:

    1. Yang, Zixuan & Wu, Baoyindureng, 2018. "Strong edge chromatic index of the generalized Petersen graphs," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 431-441.

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