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• W3127978156 abstract "A blocking set in a graph G is a subset of vertices that intersects every maximum independent set of G. Let (textsf {mmbs} (G)) be the size of a maximum (inclusion-wise) minimal blocking set of G. This parameter has recently played an important role in the kernelization of Vertex Cover with structural parameterizations. We provide a panorama of the complexity of computing (textsf {mmbs} ) parameterized by the natural parameter and the independence number of the input graph. We also consider the closely related parameter (textsf {mmhs} ), which is the size of a maximum minimal hitting set of a hypergraph. Finally, we consider the problem of computing (textsf {mmbs} ) parameterized by treewidth, especially relevant in the context of kernelization. Since a blocking set intersects every maximum-sized independent set of a given graph and properties involving counting the sizes of arbitrarily large sets are typically non-expressible in monadic second-order logic, its tractability does not seem to follow from Courcelle’s theorem. Our main technical contribution is a fixed-parameter tractable algorithm for this problem." @default.
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• W3127978156 date "2022-09-17" @default.
• W3127978156 modified "2023-10-18" @default.
• W3127978156 title "Parameterized Complexity of Computing Maximum Minimal Blocking and Hitting Sets" @default.
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• W3127978156 doi "https://doi.org/10.1007/s00453-022-01036-5" @default.
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