The maximum cardinality cut problem in co-bipartite chain graphs

Arman Boyacı (), Tınaz Ekim () and Mordechai Shalom ()
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Arman Boyacı: Bogaziçi University
Tınaz Ekim: Bogaziçi University
Mordechai Shalom: Bogaziçi University

Journal of Combinatorial Optimization, 2018, vol. 35, issue 1, No 19, 250-265

Abstract: 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.

Keywords: Maximum cut; Co-bipartite graphs; Dynamic programming; Chain graph; 68R10; 05C85 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-015-9963-x

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