Nearly perfect matchings in regular simple hypergraphs
- Cite this article as:
- Alon, N., Kim, JH. & Spencer, J. Isr. J. Math. (1997) 100: 171. doi:10.1007/BF02773639
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For every fixedk≥3 there exists a constantck with the following property. LetH be ak-uniform,D-regular hypergraph onN vertices, in which no two edges contain more than one common vertex. Ifk>3 thenH contains a matching covering all vertices but at mostckND−1/(k−1). Ifk=3, thenH contains a matching covering all vertices but at mostc3ND−1/2ln3/2D. This improves previous estimates and implies, for example, that any Steiner Triple System onN vertices contains a matching covering all vertices but at mostO(N1/2ln3/2N), improving results by various authors.