Subgraphs of colour-critical graphs

Abstract

Some problems and results on the distribution of subgraphs in colour-critical graphs are discussed.

In section 3 arbitrarily largek-critical graphs withn vertices are constructed such that, in order to reduce the chromatic number tok−2, at leastc k n 2 edges must be removed.

In section 4 it is proved that a 4-critical graph withn vertices contains at mostn triangles. Further it is proved that ak-critical graph which is not a complete graph contains a (k−1)-critical graph which is not a complete graph.

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Stiebitz, M. Subgraphs of colour-critical graphs. Combinatorica 7, 303–312 (1987). https://doi.org/10.1007/BF02579307

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AMS subject classification (1980)

  • 05 C 15
  • 05 C 35