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A characterization of Seymour graphs

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Integer Programming and Combinatorial Optimization (IPCO 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 920))

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Abstract

A connected undirected graph G is called a Seymour graph if the maximum number of edge disjoint T-cuts is equal to the cardinality of a minimum T-join for every even subset T of V(G). Several families of graphs have been shown to be subfamilies of Seymour graphs (Seymour[5][6], Gerards [1], Szigeti [7]). In this paper we prove a characterization of Seymour graphs which was conjectured by Sebö and implies the results mentioned above.

Research was partially supported by the Russian Foundation for Fundamental Research, grant 93-011-1486. The second author completed his part of the work when visiting KAM, Charles University.

Research was partially supported by the Hungarian National Foundation for Scientific Research, grants OTKA 2118 and 4271.

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References

  1. A. M. H. Gerards, On shortest T-joins and packing T-cuts, J. Comb. Theory B55 (1992) 73–82.

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  5. P. D. Seymour, The matroids with the max-flow min-cut property, J. Comb. Theory B23 (1977) 189–222.

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  7. Z. Szigeti, On Seymour Graphs, Report No. 93803-OR, Institute for Operations Research, Universität Bonn, 1993.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Universitetskii pr.4, 630090, Novosibirsk, Russia

    A. A. Ageev & A. V. Kostochka

  2. Mathematical Institute of the Hungarian Academy of Sciences, Reáltanoda u. 13-15, H-1053, Budapest, Hungary

    Z. Szigeti

Authors
  1. A. A. Ageev
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  2. A. V. Kostochka
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  3. Z. Szigeti
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Editor information

Egon Balas Jens Clausen

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© 1995 Springer-Verlag Berlin Heidelberg

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Ageev, A.A., Kostochka, A.V., Szigeti, Z. (1995). A characterization of Seymour graphs. In: Balas, E., Clausen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1995. Lecture Notes in Computer Science, vol 920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59408-6_65

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  • DOI: https://doi.org/10.1007/3-540-59408-6_65

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59408-6

  • Online ISBN: 978-3-540-49245-0

  • eBook Packages: Springer Book Archive

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