Israel Journal of Mathematics

, Volume 100, Issue 1, pp 171–187

Nearly perfect matchings in regular simple hypergraphs

Article

DOI: 10.1007/BF02773639

Cite this article as:
Alon, N., Kim, JH. & Spencer, J. Isr. J. Math. (1997) 100: 171. doi:10.1007/BF02773639

Abstract

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.

Copyright information

© Hebrew University 1997

Authors and Affiliations

  1. 1.AT & T Bell LabsMurray HillUSA
  2. 2.Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael
  3. 3.Department of Mathematics and Computer ScienceCourant InstituteNYUUSA

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