Blockers and Transversals

Abstract : We explore connections between d-blockers B in a graph G = (V;E) (i.e. subsets of edges whose removal decreases by at least d the cardinality of maximum matchings) and d-transversals T (i.e. subsets of edges such that every maximum matching M has at least d edges in T. Special classes of graphs are examined which include complete graphs, regular bipartite graphs, grid graphs, chains and cycles. We also study the complexity status of finding minimum transversals and blockers. Algorithms for d-transversals and d- blockers based on dynamic programming are given for trees.
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Submitted on : Tuesday, April 8, 2014 - 2:36:00 PM
Last modification on : Wednesday, July 3, 2019 - 10:48:04 AM

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Rico Zenklusen, Bernard Ries, Christophe Picouleau, Dominique de Werra, Marie-Christine Costa, et al.. Blockers and Transversals. Discrete Mathematics, Elsevier, 2009, 13, pp.4306--4314. ⟨10.1016/j.disc.2009.01.006⟩. ⟨hal-00975349⟩

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