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强完美图定理及相关的问题 被引量：8

Strong Perfect Graph Theorem and Questions Beyond
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摘要 介绍强完美图定理(The Strong Perfect Graph Theorem,SPGT)的历史和获证经过,同时简述SPGT被克服后生发的一些新问题,以期对图理论的一般研究起到鼓励和促进作用.因具体的证明浩大聱曲,在技术的部分仅注重框架而不涉及细节. We survey the history and proof of the Strong Perfect Graph Theorem, introducing to the Chinese mathematical community. In addition, related problems in the post SPGC era are discussed.
作者 宋春伟
机构地区 北京大学数学科学学院
出处 《数学进展》 CSCD 北大核心 2008年第2期153-162,共10页 Advances in Mathematics（China）
关键词 完美图 Berge图 SPGC 强完美图定理 perfect graph Berge graph SPGC SPGT
分类号 O157.5 [理学—基础数学]
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参考文献47

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  • 2Berge, C., Perfect graphs, Six Papers on Graph Theory: 1-21, Calcutta: Indian Statistical Institute, 1963.
  • 3Berge, C., Some classes of perfect graphs, Graph Theory and Theoretical Physics, 155-165, Academic Press, London, 1967.
  • 4Berge, C., Principes de Combinatoire, Dunod, Paris, 1968.
  • 5Berge, C. and Chvatal, V., Topics on Perfect Graphs, volume 88 of North-Holland Mathematics Studies, Annals of Discrete Mathematics, 21, North-Holland Publishing Co., Amsterdam, 1984.
  • 6Berge, C. and Ramlrez Alfonsln, J. L., Origins and Genesis, Perfect Graphs, Wiley-Intersci. Ser. Discrete Math. Optim., 1-12, Wiley, Chichester, 2001.
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  • 9Chudnovsky, M., Berge Trigraphs and Their Applications, PhD Thesis, Princeton University, 2003.
  • 10Chudnovsky, M., Perfect graphs, Available at www.aimath.org/pastworkshops/perfectgraph.html

同被引文献51

  • 1BEINEKE L W, WILSON R J. Selected topics in graph theory[M]. London: Academic Press, 1983:56-85.
  • 2BONDY J A, MURTY U S A. Graph theory with applications[M]. London:The Macmillan Press LTD, 1976.
  • 3BERGE C. Minimax theorems for normal hypergraphs and balanced hypergraphs --a survey[ J]. Annals of Discrete Mathematics, 1984, 21:3-19.
  • 4BERGE C. Graphs and hypergraphs [ M ]. Amsterdam: North-Holland Publishing Company, 1973.
  • 5BERGE C.超图[M].卜月华,张克民,译.南京:东南大学出版社,2002.
  • 6Godsil C. , Royle G. , Algebraic Graph Theory[M]. New York: Springer, 2001.
  • 7Chartrand G. , Zhang P. , Chromatic Graph Theory [ M ]. London : Taylor & Francis Group, 2009.
  • 8Brouwera A. E. , Cohen A. M. , Neumaier A. , Distance - Regular Graphs [ M ]. Berlin : Springer - Verlag, 1998.
  • 9Orel M. , Adjacency preservers, symmetric matrices, and cores[J]. J. Algebr Comb. , 2011, 35:633 -647.
  • 10Chudnovsky M. , Robertson, N. , Seymour P. D. , Thomas R. , The strong perfect graph theorem[J]. Ann. of Math., (2), 2006, 164(1) : 51 -229.

引证文献8

二级引证文献9

数学进展
2008年 第2期

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