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What must and what need not be contained in a graph of uncountable chromatic number?

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Abstract

We investigate the following problem: What countable graphs must a graph of uncountable chromatic number contain? We define two graphsΓ andΔ which are very similar and we show thatΓ is contained in every graph of uncountable chromatic number, whileΔ is (consistently) not.

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Authors and Affiliations

  1. Mathematical Institute of the, Hungarian Academy of Sciences, Pf. 428, H-1395, Budapest, Hungary

    András Hajnal

  2. Department of Algebra & Nu. Th., Eötvös University, Múzeum krt. 6–8, H-1088, Budapest, Hungary

    Péter Komjáth

Authors
  1. András Hajnal
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  2. Péter Komjáth
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Dedicated to Paul Erdős on his seventieth birthday

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Hajnal, A., Komjáth, P. What must and what need not be contained in a graph of uncountable chromatic number?. Combinatorica 4, 47–52 (1984). https://doi.org/10.1007/BF02579156

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  • DOI: https://doi.org/10.1007/BF02579156

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