Couplages et transversaux généralisés d'un hypergraphe infini |
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Authors: | Norbert Polat |
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Institution: | Centre de Mathématique Sociale, École des Hautes Études en Sciences Sociales, Marseille, France |
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Abstract: | Let be a hypergraph possibly infinite but whose edges are finite sets. An s-transversal of is a set of vertices of whose intersection with each edge A has a power greater than or equal to some cardinal s(A). Three successively stronger kinds of matchings of are defined: the s-maximal, the strongly s-maximal, and the s-perfect matchings. The first two generalize matchings of maximal cardinality, whereas a matching is s-perfect iff has an s-transversal T with T ? ∪ and |T ∩ C| = s(C) for every C ∈ . Several classes of hypergraphs having strongly s-maximal or s-perfect matchings are characterized. |
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