2026-07-22T02:03:04Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:11474 2024-03-06T10:48:07Z ddc:004 open_access

Parameterized Algorithms for Maximum Cut with Connectivity Constraints Eto, Hiroshi Hanaka, Tesshu Kobayashi, Yasuaki Kobayashi, Yusuke Maximum cut Parameterized algorithm NP-hardness Graph parameter 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Hiroshi Eto and Tesshu Hanaka and Yasuaki Kobayashi and Yusuke Kobayashi 2019 Is Part Of LIPIcs, Volume 148, 14th International Symposium on Parameterized and Exact Computation (IPEC 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.IPEC.2019.13 urn:nbn:de:0030-drops-114747 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2019.13 eng https://creativecommons.org/licenses/by/3.0/legalcode