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Some remarks on (k−1)-critical subgraphs ofk-critical graphs

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Abstract

A graphG is said to bek-critical if it has chromatic numberk, but every proper subgraph ofG has a (k−1)-coloring. Gallai asked whether every largek-critical graph contains many (k−1)-critical subgraphs. We provide some information concerning this question and some related questions.

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Authors and Affiliations

  1. Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Alberta, Canada

    H. L. Abbott

  2. Department of Mathematics, Trent University, K9J 7B8, Peterborough, Ontario, Canada

    B. Zhou

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  1. H. L. Abbott
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  2. B. Zhou
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Abbott, H.L., Zhou, B. Some remarks on (k−1)-critical subgraphs ofk-critical graphs. Combinatorica 15, 469–474 (1995). https://doi.org/10.1007/BF01192519

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  • DOI: https://doi.org/10.1007/BF01192519

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