Couplages et transversaux généralisés d'un hypergraphe infini

Let $\text{A}$ be a hypergraph possibly infinite but whose edges are finite sets. An s-transversal of $\text{A}$ is a set of vertices of $\text{A}$ 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 $\text{A}$ 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 $\text{C}$ is s-perfect iff $\text{A}$ has an s-transversal T with T ? ∪ $\text{C}$ and |T ∩ C| = s(C) for every C ∈ $\text{C}$. Several classes of hypergraphs having strongly s-maximal or s-perfect matchings are characterized.