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Combinatorial Optimization — Eureka, You Shrink! pp 39–47Cite as

Hajós’ Construction and Polytopes

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2570))

Abstract

Odd cycles are well known to induce facet-defining inequalities for the stable set polytope. In graph coloring odd cycles represent the class of 3-critical graphs. We study Hajós’ construction to obtain a large class of n-critical graphs (n > 3), which properly generalize both cliques and odd cycles, and which again turn out to be facet-inducing for the associated stable set polytope.

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References

  1. G. Hajós. Über eine Konstruktion nicht n-färbbarer Graphen. Wiss.Z.Martin-Luther-Univ.Halle-Wittenberg, Math.-Naturw. Reihe 10, 116–117, 1961.

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  2. J. Edmonds. Minimum Partition of a Matroid into Independent Subsets. Journal of Research of the National Bureau of Standards 69B, 67–72, 1965.

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  3. V. Chvàtal. On certain polytopes associated with graphs. J.Comb.Theory B 18, 138–154, 1975.

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  4. T.R. Jensen B. Toft. Graph Coloring Problems. Wiley, New York, 1995.

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  5. R. Euler. Coloring planar Toeplitz graphs and the stable set polytope. Working paper, presented at the 17th International Symposium on Mathematical Programming, Atlanta, 2000, and the 6th International Conference on Graph Theory, Marseille, 2000 (submitted).

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Author information

Authors and Affiliations

  1. Faculté des Sciences, 20 Avenue Le Gorgeu, 29285, Brest Cedex, France

    Reinhardt Euler

Authors
  1. Reinhardt Euler
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Editors and Affiliations

  1. Institut für Informatik, Universität zu Köln, Pohligstr. 1, 50969, Köln, Germany

    Michael Jünger

  2. Institut für Informatik, Universität Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Gerhard Reinelt

  3. Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti”, CNR, viale Manzoni 30, 00185, Rome, Italy

    Giovanni Rinaldi

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© 2003 Springer-Verlag Berlin Heidelberg

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Euler, R. (2003). Hajós’ Construction and Polytopes. In: Jünger, M., Reinelt, G., Rinaldi, G. (eds) Combinatorial Optimization — Eureka, You Shrink!. Lecture Notes in Computer Science, vol 2570. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36478-1_6

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  • DOI: https://doi.org/10.1007/3-540-36478-1_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00580-3

  • Online ISBN: 978-3-540-36478-8

  • eBook Packages: Springer Book Archive

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