Abstract:Let H = (V, E) be an r-uniform hypergraph on n vertices and fix a positive integer k such that 1 ≤ k ≤ r. A k-matching of H is a collection of edges M ⊂ E such that every subset of V whose cardinality equals k is contained in at most one element of M. The k-matching number of H is the maximum cardinality of a k-matching. A well-known problem, posed by Erdős, asks for the maximum number of edges in an r-uniform hypergraph under constraints on its 1-matching number. In this article we investigate the more genera… Show more
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