Both connectivity-constrained cut problems are NP-complete on planar bipartite and split graphs, yet they are fixed-parameter tractable in treewidth, twin-cover number, and solution size.
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Parameterized Algorithms for Maximum Cut with Connectivity Constraints
Both connectivity-constrained cut problems are NP-complete on planar bipartite and split graphs, yet they are fixed-parameter tractable in treewidth, twin-cover number, and solution size.