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On Finding the Maximum Number of Disjoint Cuts in Seymour Graphs

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Algorithms - ESA’ 99 (ESA 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1643))

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Abstract

In the CUT PACKING problem, given an undirected connected graph G, it is required to find the maximum number of pairwise edge disjoint cuts in G. It is an open question if CUT PACKING is NP-hard on general graphs. In this paper we prove that the problem is polynomially solvable on Seymour graphs which include both all bipartite and all series-parallel graphs. We also consider the weighted version of the problem in which each edge of the graph G has a nonnegative weight and the weight of a cut D is equal to the maximum weight of edges in D. We show that the weighted version is NP-hard even on cubic planar graphs.

This research was partially supported by the Russian Foundation for Basic Research, grants 97-01-00890, 99-01-00601.

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Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Koptyuga 4, 630090, Novosibirsk, Russia

    Alexander A. Ageev

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  1. Alexander A. Ageev
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Editors and Affiliations

  1. Department of Applied Mathematics and DIMATIA Centre, Charles University, Malostranská nám. 25, CZ-11800, Prague 1, Czech Republic

    Jaroslav Nešetřil

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© 1999 Springer-Verlag Berlin Heidelberg

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Ageev, A.A. (1999). On Finding the Maximum Number of Disjoint Cuts in Seymour Graphs. In: Nešetřil, J. (eds) Algorithms - ESA’ 99. ESA 1999. Lecture Notes in Computer Science, vol 1643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48481-7_42

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  • DOI: https://doi.org/10.1007/3-540-48481-7_42

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66251-8

  • Online ISBN: 978-3-540-48481-3

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