Israel Journal of Mathematics

, Volume 61, Issue 3, pp 285–294 | Cite as

Consistency results on infinite graphs

  • Péter Komjáth
Article

Abstract

Consistently there exist ℵ2-chromatic graphs with no ℵ1-chromatic subgraphs. The statement that every uncountably chromatic graph of size ℵ1 contains an uncountably chromaticω-connected subgraph is consistent and independent. It is consistent that there is an uncountably chromatic graph of size ℵω 1 in which every subgraph with size less than ℵω 1 is countably chromatic.

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Copyright information

© Hebrew University 1988

Authors and Affiliations

  • Péter Komjáth
    • 1
    • 2
  1. 1.Department of MathematicsLehigh UniversityBethlehemUSA
  2. 2.Department of Computer ScienceEötvös UniversityBudapestHungary

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