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Graphs and Combinatorics pp 243–246Cite as

The minimality of the mycielski graph

  • Part III: Contributed Papers New Results On Graphs And Combinatorics
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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 406))

Abstract

It is proved that the smallest 4-chromatic triangle — free graph has eleven vertices and is unique.

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References

  1. Brooks, R. L., On Colouring the Nodes of a Network, Proc. Cambridge Phil. Soc. 37 (1941), 194–197.

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  2. Chvátal, V., The Smallest Triangle-free 4-chromatic 4-regular Graph, J. Com J. Combinatorial Theory 9 (1970), 93–94.

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  3. Erdös, P., Graph Theory and Probability, Canad. J. Math. 11 (1959), 34–38.

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  4. Harary, F., Graph Theory, Addison-Wesley, Reading, Mass., 1969, p. 149, Exercise 12.19.

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  5. Lovász, L., On the Chromatic Number of Finite Set-systems, Acta. Math. Acad. Sci. Hungar. 19 (1968), 59–67.

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  6. Mycielski, J., Sur le coloriage des graphes, Colloq. Math. 3 (1955), 161–162.

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Author information

Authors and Affiliations

  1. Centre de Recherches Mathématiques, Université de Montréal, Montréal 101, Canada

    V. Chvátal

Authors
  1. V. Chvátal
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Editor information

Ruth A. Bari Frank Harary

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© 1974 Springer-Verlag Berlin

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Chvátal, V. (1974). The minimality of the mycielski graph. In: Bari, R.A., Harary, F. (eds) Graphs and Combinatorics. Lecture Notes in Mathematics, vol 406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066446

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  • DOI: https://doi.org/10.1007/BFb0066446

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06854-9

  • Online ISBN: 978-3-540-37809-9

  • eBook Packages: Springer Book Archive

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