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The maximum cardinality cut problem in co-bipartite chain graphs

Author

Listed:
  • Arman Boyacı

    (Bogaziçi University)

  • Tınaz Ekim

    (Bogaziçi University)

  • Mordechai Shalom

    (Bogaziçi University
    TelHai College)

Abstract

A co-bipartite chain graph is a co-bipartite graph in which the neighborhoods of the vertices in each clique can be linearly ordered with respect to inclusion. It is known that the maximum cardinality cut problem ( $${\textsc {MaxCut}}$$ M A X C U T ) is $${\textsc {NP}}{\text {-hard}}$$ NP -hard in co-bipartite graphs (Bodlaender and Jansen, Nordic J Comput 7(2000):14–31, 2000). We consider $${\textsc {MaxCut}}$$ M A X C U T in co-bipartite chain graphs. We first consider the twin-free case and present an explicit solution. We then show that $${\textsc {MaxCut}}$$ M A X C U T is polynomial time solvable in this graph class.

Suggested Citation

  • Arman Boyacı & Tınaz Ekim & Mordechai Shalom, 2018. "The maximum cardinality cut problem in co-bipartite chain graphs," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 250-265, January.
    • Handle: RePEc:spr:jcomop:v:35:y:2018:i:1:d:10.1007_s10878-015-9963-x
    DOI: 10.1007/s10878-015-9963-x
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    References listed on IDEAS

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