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Submodular Functions and Perfect Graphs

Author

Listed:
  • Tara Abrishami

    (Department of Mathematics, University of Hamburg, 20148 Hamburg, Germany)

  • Maria Chudnovsky

    (Department of Mathematics, Princeton University, Princeton, New Jersey 08544)

  • Cemil Dibek

    (Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544)

  • Kristina Vušković

    (School of Computing, University of Leeds, Leeds LS2 9JT, United Kingdom)

Abstract

We give a combinatorial polynomial-time algorithm to find a maximum weight independent set in perfect graphs of bounded degree that do not contain a prism or a hole of length four as an induced subgraph. An even pair in a graph is a pair of vertices all induced paths between which are even. An even set is a set of vertices every two of which are an even pair. We show that every perfect graph that does not contain a prism or a hole of length four as an induced subgraph has a balanced separator which is the union of a bounded number of even sets, where the bound depends only on the maximum degree of the graph. This allows us to solve the maximum weight independent set problem using the well-known submodular function minimization algorithm.

Suggested Citation

  • Tara Abrishami & Maria Chudnovsky & Cemil Dibek & Kristina Vušković, 2025. "Submodular Functions and Perfect Graphs," Mathematics of Operations Research, INFORMS, vol. 50(1), pages 189-208, February.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:1:p:189-208
    DOI: 10.1287/moor.2021.0302
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