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On circuits and subgraphs of chromatic graphs

  • P. Erdös (a1)
Abstract

A graph is said to be k-chromatic if its vertices can be split into k classes so that two vertices of the same class are not connected (by an edge) and such a splitting is not possible for k−1 classes. Tutte was the first to show that for every k there is a k-chromatic graph which contains no triangle [1].

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2. J. B. Kelly and L. M. Kelly , “Paths and circuits in critical graphs”, American J. of Math., 76 (1954), 786792.

3. P. Erdös , “Graph theory and probability”, Canadian J. of Math., 11 (1959), 3438.

5. P. Erdös and G. Szekeres , “Graph theory and probability (II)”, Canadian J. of Math., 13 (1961), 346352.

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Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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