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The Cycling Property for the Clutter of Odd st-Walks

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Integer Programming and Combinatorial Optimization (IPCO 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8494))

Abstract

A binary clutter is cycling if its packing and covering linear program have integral optimal solutions for all eulerian edge capacities. We prove that the clutter of odd st-walks of a signed graph is cycling if and only if it does not contain as a minor the clutter of odd circuits of K 5 nor the clutter of lines of the Fano matroid. Corollaries of this result include, of many, the characterization for weakly bipartite signed graphs [5], packing two-commodity paths[7,10], packing T-joins with small |T|, a new result on covering odd circuits of a signed graph, as well as a new result on covering odd circuits and odd T-joins of a signed graft.

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Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, Canada

    Ahmad Abdi & Bertrand Guenin

Authors
  1. Ahmad Abdi
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  2. Bertrand Guenin
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Editors and Affiliations

  1. Department of Industrial and Operations Engineering, University of Michigan, Beal Avenue, 1205, Ann Arbor, MI, USA

    Jon Lee

  2. Research Institute for Discrete Mathematics, University of Bonn, Lennéstr. 2, P.O. Box, 53113, Bonn, Germany

    Jens Vygen

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© 2014 Springer International Publishing Switzerland

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Abdi, A., Guenin, B. (2014). The Cycling Property for the Clutter of Odd st-Walks. In: Lee, J., Vygen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2014. Lecture Notes in Computer Science, vol 8494. Springer, Cham. https://doi.org/10.1007/978-3-319-07557-0_1

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  • DOI: https://doi.org/10.1007/978-3-319-07557-0_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07556-3

  • Online ISBN: 978-3-319-07557-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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