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On circuits and subgraphs of chromatic graphs

  • P. Erdös (a1)

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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1. Blanche Descartes, “A three colour problem”, Eureka (April 1947). Solution March 1948. See also Mycielski J., “Sur le colorage des graphs”, Colloquium Math., 3 (1955), 161162
2. Kelly J. B. and Kelly L. M., “Paths and circuits in critical graphs”, American J. of Math., 76 (1954), 786792.
3. Erdös P., “Graph theory and probability”, Canadian J. of Math., 11 (1959), 3438.
4. Erdös P. and Szekeres G., “A combinatorial problem in geometry”, Comp. Math., 2 (1935), 463470.
5. Erdös P. and Szekeres G., “Graph theory and probability (II)”, Canadian J. of Math., 13 (1961), 346352.
6. Erdös P. and Rényi A., “On the evolution of random graphs”, Pub. Mat. Inst. Hung. Acad., 5 (1960), 1761. See also the paper quoted in [3] and [5].
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  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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