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Wheel inequalities for stable set polytopes

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Abstract

We introduce new classes of valid inequalities, called wheel inequalities, for the stable set polytopeP G of a graphG. Each “wheel configuration” gives rise to two such inequalities. The simplest wheel configuration is an “odd” subdivisionW of a wheel, and for these we give necessary and sufficient conditions for the wheel inequality to be facet-inducing forP W . Generalizations arise by allowing subdivision paths to intersect, and by replacing the “hub” of the wheel by a clique. The separation problem for these inequalities can be solved in polynomial time.

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Authors and Affiliations

  1. Department of Computational and Applied Mathematics, Rice University, 77005, Houston, TX, USA

    Eddie Cheng

  2. Department of Combinatorics & Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    William H. Cunningham

Authors
  1. Eddie Cheng
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  2. William H. Cunningham
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Additional information

Research partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada.

Research partially supported by scholarships from the Ontario Ministry of Colleges and Universities.

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Cheng, E., Cunningham, W.H. Wheel inequalities for stable set polytopes. Mathematical Programming 77, 389–421 (1997). https://doi.org/10.1007/BF02614623

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  • DOI: https://doi.org/10.1007/BF02614623

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