The maximum cardinality cut problem in co-bipartite chain graphs

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 () is in co-bipartite graphs (Bodlaender and Jansen, Nordic J Comput 7(2000):14-31, 2000). We consider in co-bipartite chain graphs. We first consider the twin-free case and present an explicit solution. We then show that is polynomial time solvable in this graph class.