2026-07-23T10:34:45Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18556 2024-03-06T11:02:06Z ddc:004 open_access

MaxCut Above Guarantee Bliznets, Ivan Epifanov, Vladislav Tripartite 3-colorable chordal maximum cut FPT-algorithm linear kernel In this paper, we study the computational complexity of the Maximum Cut problem parameterized above guarantee. Our main result provides a linear kernel for the Maximum Cut problem in connected graphs parameterized above the spanning tree. This kernel significantly improves the previous O(k⁵) kernel given by Madathil, Saurabh, and Zehavi [ToCS 2020]. We also provide subexponential running time algorithms for this problem in special classes of graphs: chordal, split, and co-bipartite. We complete the picture by lower bounds under the assumption of the ETH. Moreover, we initiate a study of the Maximum Cut problem above 2/3|E| lower bound in tripartite graphs. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ivan Bliznets and Vladislav Epifanov 2023 Is Part Of LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2023.22 urn:nbn:de:0030-drops-185560 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.22 eng https://creativecommons.org/licenses/by/4.0/legalcode