{"oa":1,"license":"https://creativecommons.org/licenses/by/4.0/","doi":"10.1007/s00453-025-01306-y","OA_place":"publisher","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00453-025-01306-y"}],"_id":"19603","has_accepted_license":"1","author":[{"first_name":"Jonas","full_name":"Lill, Jonas","last_name":"Lill"},{"last_name":"Petrova","id":"554ff4e4-f325-11ee-b0c4-a10dbd523381","full_name":"Petrova, Kalina H","first_name":"Kalina H"},{"full_name":"Weber, Simon","first_name":"Simon","last_name":"Weber"}],"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","day":"10","acknowledgement":"Kalina Petrova is supported by the Swiss National Science Foundation, grant no. CRSII5 173721, and also receives funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413. Simon Weber is supported by the Swiss National Science Foundation under project no. 204320.\r\nOpen access funding provided by Swiss Federal Institute of Technology Zurich.","ec_funded":1,"OA_type":"hybrid","publication_status":"epub_ahead","language":[{"iso":"eng"}],"publisher":"Springer Nature","article_type":"original","date_updated":"2025-04-22T07:08:33Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"project":[{"call_identifier":"H2020","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"quality_controlled":"1","related_material":{"record":[{"status":"public","id":"18758","relation":"earlier_version"}]},"date_created":"2025-04-20T22:01:28Z","department":[{"_id":"MaKw"}],"date_published":"2025-04-10T00:00:00Z","oa_version":"Published Version","abstract":[{"lang":"eng","text":"MaxCut is a classical NP-complete problem and a crucial building block in many\r\ncombinatorial algorithms. The famousEdwards-Erdös bound states that any connected\r\ngraph on n vertices with m edges contains a cut of size at least m/2 + n−1/4 . Crowston,\r\nJones and Mnich [Algorithmica, 2015] showed that the MaxCut problem on simple\r\nconnected graphs admits an FPT algorithm, where the parameter k is the difference\r\nbetween the desired cut size c and the lower bound given by the Edwards-Erdös\r\nbound. This was later improved by Etscheid and Mnich [Algorithmica, 2017] to run\r\nin parameterized linear time, i.e., f (k) · O(m). We improve upon this result in two\r\nways: Firstly, we extend the algorithm to work also for multigraphs (alternatively,\r\ngraphs with positive integer weights). Secondly, we change the parameter; instead of\r\nthe difference to the Edwards-Erdös bound, we use the difference to the Poljak-Turzík\r\nbound. The Poljak-Turzík bound states that any weighted graph G has a cut of weight\r\nat least w(G)/2 + wMSF (G)/4 , where w(G) denotes the total weight of G, and wMSF (G)\r\ndenotes the weight of its minimum spanning forest. In connected simple graphs the\r\ntwo bounds are equivalent, but for multigraphs the Poljak-Turzík bound can be larger\r\nand thus yield a smaller parameter k. Our algorithm also runs in parameterized linear\r\ntime, i.e., f (k) · O(m + n)."}],"title":"Linear-time MaxCut in multigraphs parameterized above the Poljak-Turzík bound","publication":"Algorithmica","month":"04","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2025","status":"public","type":"journal_article","publication_identifier":{"issn":["0178-4617"],"eissn":["1432-0541"]}}