Parameterized Algorithms for Maximum Cut with Connectivity Constraints

Abstract

We study two variants of Maximum Cut, which we call Connected Maximum Cut and Maximum Minimal Cut, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some connectivity requirements. Both problems are known to be NPcomplete even on planar graphs whereas Maximum Cut on planar graphs is solvable in polynomial time. We first show that these problems are NP-complete even on planar bipartite graphs and split graphs. Then we give parameterized algorithms using graph parameters such as clique-width, tree-width, and twin-cover number. Finally, we obtain FPT algorithms with respect to the solution size. ACM Subject Classification Mathematics of computing → Graph algorithmsKeywords and phrases Maximum cut, Parameterized algorithm, NP-hardness, Graph parameter Acknowledgements We thank Akitoshi Kawamura and Yukiko Yamauchi for giving an opportunity to discuss in the Open Problem Seminar in Kyushu University.