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


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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Abbott, H.L., Zhou, B. Some remarks on (k−1)-critical subgraphs ofk-critical graphs. Combinatorica 15, 469–474 (1995).

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Mathematics Subject Classification (1991)

  • 05 C 15
  • 05 C 35