Parameterized Algorithms for Maximum Cut with Connectivity Constraints

Authors Hiroshi Eto, Tesshu Hanaka , Yasuaki Kobayashi, Yusuke Kobayashi

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Hiroshi Eto
  • Kyushu University, Fukuoka, Japan
Tesshu Hanaka
  • Chuo University, Tokyo, Japan
Yasuaki Kobayashi
  • Kyoto University, Kyoto, Japan
Yusuke Kobayashi
  • Kyoto University, Kyoto, Japan


We thank Akitoshi Kawamura and Yukiko Yamauchi for giving an opportunity to discuss in the Open Problem Seminar at Kyushu University. This work is partially supported by JST CREST JPMJCR1401 and JSPS KAKENHI Grant Numbers JP17H01788, JP18H06469, JP16K16010, JP17K19960, and JP18H05291.

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Hiroshi Eto, Tesshu Hanaka, Yasuaki Kobayashi, and Yusuke Kobayashi. Parameterized Algorithms for Maximum Cut with Connectivity Constraints. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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 NP-complete 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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Maximum cut
  • Parameterized algorithm
  • NP-hardness
  • Graph parameter


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