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 (\({\textsc {MaxCut}}\)) is \({\textsc {NP}}{\text {-hard}}\) in co-bipartite graphs (Bodlaender and Jansen, Nordic J Comput 7(2000):14–31, 2000). We consider \({\textsc {MaxCut}}\) in co-bipartite chain graphs. We first consider the twin-free case and present an explicit solution. We then show that \({\textsc {MaxCut}}\) is polynomial time solvable in this graph class.
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Notes
This is the only fact about treewidth used in this work.
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Acknowledgments
This work is supported in part by TUBITAK Career Project Grant Nos. 111M482, and TUBITAK 2221 Program.
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Boyacı, A., Ekim, T. & Shalom, M. The maximum cardinality cut problem in co-bipartite chain graphs. J Comb Optim 35, 250–265 (2018). https://doi.org/10.1007/s10878-015-9963-x
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DOI: https://doi.org/10.1007/s10878-015-9963-x