Linear-time MaxCut in multigraphs parameterized above the Poljak-Turzík bound LIPIcs Lill, Jonas Petrova, Kalina H Weber, Simon ddc:500 MaxCut is a classical NP-complete problem and a crucial building block in many combinatorial algorithms. The famous Edwards-Erdős bound states that any connected graph on n vertices with m edges contains a cut of size at least m/2+(n-1)/4. Crowston, Jones and Mnich [Algorithmica, 2015] showed that the MaxCut problem on simple connected graphs admits an FPT algorithm, where the parameter k is the difference between the desired cut size c and the lower bound given by the Edwards-Erdős bound. This was later improved by Etscheid and Mnich [Algorithmica, 2017] to run in parameterized linear time, i.e., f(k)⋅ O(m). We improve upon this result in two ways: Firstly, we extend the algorithm to work also for multigraphs (alternatively, graphs with positive integer weights). Secondly, we change the parameter; instead of the difference to the Edwards-Erdős bound, we use the difference to the Poljak-Turzík bound. The Poljak-Turzík bound states that any weighted graph G has a cut of size at least (w(G))/2+(w_MSF(G))/4, where w(G) denotes the total weight of G, and w_MSF(G) denotes the weight of its minimum spanning forest. In connected simple graphs the two bounds are equivalent, but for multigraphs the Poljak-Turzík bound can be larger and thus yield a smaller parameter k. Our algorithm also runs in parameterized linear time, i.e., f(k)⋅ O(m+n). Schloss Dagstuhl - Leibniz-Zentrum für Informatik 2024 info:eu-repo/semantics/conferenceObject doc-type:ConferenceObject ConferenceObject http://purl.org/coar/resource_type/c_5794 https://research-explorer.ista.ac.at/record/18758 https://research-explorer.ista.ac.at/download/18758/18775 Lill J, Petrova KH, Weber S. Linear-time MaxCut in multigraphs parameterized above the Poljak-Turzík bound. In: <i>19th International Symposium on Parameterized and Exact Computation</i>. Vol 321. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href="https://doi.org/10.4230/LIPIcs.IPEC.2024.2">10.4230/LIPIcs.IPEC.2024.2</a> eng info:eu-repo/semantics/altIdentifier/doi/10.4230/LIPIcs.IPEC.2024.2 info:eu-repo/semantics/altIdentifier/issn/1868-8969 info:eu-repo/semantics/altIdentifier/isbn/9783959773539 info:eu-repo/semantics/altIdentifier/wos/001534851900002 info:eu-repo/semantics/altIdentifier/arxiv/2407.01071 info:eu-repo/semantics/openAccess