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Israel Journal of Mathematics

, Volume 56, Issue 3, pp 257–266 | Cite as

Connectivity and chromatic number of infinite graphs

  • Péter Komjáth
Article

Abstract

Every graph with uncountable chromatic number contains for every finiten ann-connected subgraph with infinite degrees which has uncountable chromatic number.

Keywords

Correct Order Chromatic Number Compactness Theorem Free Algebra Subgraph Isomorphic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    S. Ben-David,On Shelah’s compactness of cardinals, Isr. J. Math.31 (1978), 34–56.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    P. Erdõs and A. Hajnal,On chromatic number of graphs and set-systems, Acta Math. Acad. Sci. Hung.17 (1966), 61–99.CrossRefGoogle Scholar
  3. 3.
    W. Hodges,In singular cardinality, locally free algebras are free, Algebra Univ.12 (1981), 205–220.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    P. Komjáth,The coloring number, Proc. London Math. Soc., to appear.Google Scholar
  5. 5.
    E. W. Miller,On a propery of families of sets, Comptes Rendus Varsovie30 (1937), 31–38.zbMATHGoogle Scholar
  6. 6.
    S. Shelah,A compactness theorem for singular cardinals, free algebras, Whitehead problem, and transversals, Isr. J. Math.21 (1975), 319–349.zbMATHCrossRefGoogle Scholar

Copyright information

© Hebrew University 1986

Authors and Affiliations

  • Péter Komjáth
    • 1
  1. 1.Department of Computer ScienceR. Eötvös University, Institute of MathematicsBudapestHungary

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