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Polyhedral results on the stable set problem in graphs containing even or odd pairs

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Abstract

Even and odd pairs are important tools in the study of perfect graphs and were instrumental in the proof of the Strong Perfect Graph Theorem. We suggest that such pairs impose a lot of structure also in arbitrary, not just perfect graphs. To this end, we show that the presence of even or odd pairs in graphs imply a special structure of the stable set polytope. In fact, we give a polyhedral characterization of even and odd pairs.

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Authors and Affiliations

  1. Operations Research, RWTH Aachen University, Aachen, Germany

    Jonas T. Witt & Marco E. Lübbecke

  2. Laboratoire I3S CNRS, Sophia-Antipolis, France

    Bruce Reed

  3. IMPA, Rio de Janeiro, Brazil

    Bruce Reed

Authors
  1. Jonas T. Witt
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  2. Marco E. Lübbecke
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  3. Bruce Reed
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Correspondence to Marco E. Lübbecke.

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Witt, J.T., Lübbecke, M.E. & Reed, B. Polyhedral results on the stable set problem in graphs containing even or odd pairs. Math. Program. 171, 519–522 (2018). https://doi.org/10.1007/s10107-017-1168-x

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  • DOI: https://doi.org/10.1007/s10107-017-1168-x

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