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

Short Communication Series A

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.

Keywords

Stable set problem Stable set polytope Even pairs Odd pairs Integer programming 

Mathematics Subject Classification

90C10 (Integer programming) 90C27 (Combinatorial optimization) 90C57 (Polyhedral combinatorics, branch-and-bound, branch-and-cut) 

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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2017

Authors and Affiliations

  • Jonas T. Witt
    • 1
  • Marco E. Lübbecke
    • 1
  • Bruce Reed
    • 2
    • 3
  1. 1.Operations ResearchRWTH Aachen UniversityAachenGermany
  2. 2.Laboratoire I3S CNRSSophia-AntipolisFrance
  3. 3.IMPARio de JaneiroBrazil

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