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3-临界图独立数的一个结果

A Result on Independence Number of 3-Critical Graph
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摘要 1968年,Vizing提出了关于临界图的独立数猜想:若G是n阶的Δ-临界图,则有α(G)≤n/2.利用Vizing邻接引理研究这一猜想,给出了3-临界图的一个上界. In 1968, Vizing conjectured that if G is a A - critical graph with n vertices, then: a(G) ≤n/2, where a(G) is the independence number of G. In this paper, we give an upper bound of the independence number of 3 - critical graph.
出处 《四川文理学院学报》 2012年第2期21-22,共2页 Sichuan University of Arts and Science Journal
基金 中央高校基本科研业务费专项基金(2010LKSX06)
关键词 边染色 临界图 独立数 edge coloring critical graph independence number
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参考文献8

  • 1Vizing V G.Critical Graphs with a Given Chromatic Index[J].Diskret Analiz,1965(5):9-17.
  • 2Vizing V G.Some Unsolved Problems in Graph Theory[J].Russian Math Surveys,1968(6):125-141.
  • 3Brinkmann G,Choudum S A,Grünewald S,et al.Bounds for the Independence Number of Critical Graphs[J].Bull LondonMath Soc,2000(2):137-140.
  • 4Grünewald S,Steffen E.Independent Sets and 2-factors in Edge-chromatic-critical Graphs[J].J Graph Theory,2004(2):113-118.
  • 5Luo Rong,Zhao Yue.A Note on Vizing's Independence Number Conjecture of Edge Chromatic Critical Graphs[J].DiscreteMath,2006(15):1788-1790.
  • 6Luo Rong,Zhao Yue.An Application of Vizing and Vizing-like Adjacency Lemmas to Vizing's Independence Number Conjectureof Edge Chromatic Critical Graphs[J].Discrete Math,2009(9):2925-2929.
  • 7逄世友,马国翼,苗连英.临界图独立数的上界[J].徐州师范大学学报(自然科学版),2010,28(1):15-16. 被引量:3
  • 8Douglas R W.The Independence Number of an Edge-Chromatic Critical Graph[J].J Graph Theory,2010(2):98-103.

二级参考文献5

  • 1Vizing V G. Critical graphs with a given chromatic index[J]. Diskret Analiz, 1965 (5) :9.
  • 2Vizing V G. Some unsolved problems in graph theory[J]. Russian Math Surveys, 1968,23 (6) : 125.
  • 3Brinkmann G,Choudum S A,Griinewald S,et al. Bounds for the independence number of critical graphs[J]. Bull London Math Soc,2000,32(2) :137.
  • 4Grunewald S, Steffen E. Independent sets and 2-factors in edge-chromatic-critical graphs[J]. J Graph Theory, 2004,45 (2):113.
  • 5Luo Rong,Zhao Yue. A note on Vizing's independence number conjecture of edge chromatic critical graphs[J]. Discrete Math,2006,306(15) :1788.

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