For every fixed k ≥ 3 there exists a constant ck with the following property. Let H be a k-uniform, D-regular hypergraph on N vertices, in which no two edges contain more than one common vertex. If k > 3 then H contains a matching covering all vertices but at most ckND-1/(k-1). If k = 3, then H contains a matching covering all vertices but at most c3ND-1/2ln3/2D. This improves previous estimates and implies, for example, that any Steiner Triple System on N vertices contains a matching covering all vertices but at most 0(N1/2ln3/2N), improving results by various authors.
|Original language||English (US)|
|Number of pages||17|
|Journal||Israel Journal of Mathematics|
|State||Published - Jan 1 1997|
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