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Consistency results on infinite graphs

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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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Authors and Affiliations

  1. Department of Mathematics, Lehigh University, 18015, Bethlehem, PA, USA

    Péter Komjáth

  2. Department of Computer Science, Eötvös University, P.O. Box 323, 1445, Budapest, Hungary

    Péter Komjáth

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  1. Péter Komjáth
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Partially supported by Hungarian Science Research Fund Nu. 1805.

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Komjáth, P. Consistency results on infinite graphs. Israel J. Math. 61, 285–294 (1988). https://doi.org/10.1007/BF02772573

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  • DOI: https://doi.org/10.1007/BF02772573

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