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.
@InProceedings{bliznets_et_al:LIPIcs.MFCS.2023.22, author = {Bliznets, Ivan and Epifanov, Vladislav}, title = {{MaxCut Above Guarantee}}, booktitle = {48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)}, pages = {22:1--22:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-292-1}, ISSN = {1868-8969}, year = {2023}, volume = {272}, editor = {Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.22}, URN = {urn:nbn:de:0030-drops-185560}, doi = {10.4230/LIPIcs.MFCS.2023.22}, annote = {Keywords: Tripartite, 3-colorable, chordal, maximum cut, FPT-algorithm, linear kernel} }
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