数学季刊 ›› 2010, Vol. 25 ›› Issue (4): 510-514.

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无6-圈平面图的不完全选色性

  

  1. Department of Mathematics, Huaiyin Teacher’s College

  • 收稿日期:2006-10-25 出版日期:2010-12-30 发布日期:2023-05-17
  • 作者简介:ZHANG Hai-hui(1979-), male, native of Taixing, Jiangsu, a lecturer of Huaiyin Teacher’s College, M.S.D., engages in graph theory.
  • 基金资助:
    Supported by the Natural Science Research Project of Ordinary Universities in Jiangsu(08KJB110002); Supported by the Program for ETHYTC(08QNZCK03); Supported by the NSFC(10671095);

Improper Choosability of Planar Graphs without 6-circuits

  1. Department of Mathematics, Huaiyin Teacher’s College
  • Received:2006-10-25 Online:2010-12-30 Published:2023-05-17
  • About author:ZHANG Hai-hui(1979-), male, native of Taixing, Jiangsu, a lecturer of Huaiyin Teacher’s College, M.S.D., engages in graph theory.
  • Supported by:
    Supported by the Natural Science Research Project of Ordinary Universities in Jiangsu(08KJB110002); Supported by the Program for ETHYTC(08QNZCK03); Supported by the NSFC(10671095);

摘要: A graph G is called (k,d)*-choosable if for every list assignment L satisfying |L(v)|=k for all v ∈ V(G), there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. In this paper, it is shown that every planar graph without 6-circuits and a triangle adjacent to itself or a quadrangle is (3,1)*-choosable.

关键词:


Abstract: A graph G is called (k,d)*-choosable if for every list assignment L satisfying |L(v)|=k for all v ∈ V(G), there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. In this paper, it is shown that every planar graph without 6-circuits and a triangle adjacent to itself or a quadrangle is (3,1)*-choosable.

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