Partial Steiner systems and matchings in hypergraphs

  1. A.V. Kostochka1,*,
  2. V. Rödl2

Article first published online: 7 DEC 1998

DOI: 10.1002/(SICI)1098-2418(199810/12)13:3/4<335::AID-RSA8>3.0.CO;2-W

Issue

Random Structures & Algorithms

Random Structures & Algorithms

Special Issue: Proceedings of the Eighth International Conference “Random Structures and Algorithms” held August 4–9, 1997, in Poznan, Poland

Volume 13, Issue 3-4, pages 335–347, October - December 1998

Additional Information

How to Cite

Kostochka, A. and Rödl, V. (1998), Partial Steiner systems and matchings in hypergraphs. Random Structures & Algorithms, 13: 335–347. doi: 10.1002/(SICI)1098-2418(199810/12)13:3/4<335::AID-RSA8>3.0.CO;2-W

Author Information

  1. 1

    Institute of Mathematics, Siberian Branch of the RAS, Novosibirsk-90, 630090, Russia

  2. 2

    Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322

*Institute of Mathematics, Siberian Branch of the RAS, Novosibirsk-90, 630090, Russia

Publication History

  1. Issue published online: 7 DEC 1998
  2. Article first published online: 7 DEC 1998
  3. Manuscript Accepted: 21 JUL 1998
  4. Manuscript Received: 1 OCT 1997

Funded by

  • Cooperative Grant Program of the Civilian Research and Development Foundation. Grant Number: MR1-181
  • Russian Foundation for Fundamental Research. Grant Numbers: 96-01-01614, 97-01-01075
  • National Science Foundation. Grant Number: DMS 97-04114

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Keywords:

  • Steiner systems;
  • hypergraph matchings

Abstract

For t<k, a (t, k) T-system is a k-uniform hypergraph H such that any two distinct edges of H have at most t−1 vertices in common. Clearly, any (t, k)-system on n vertices has at most equation image edges. It was proved by Rödl that there are (t, k)-systems on n vertices with equation image edges. Then stronger results and generalizations were obtained by several authors. In particular, Grable proved that every D-regular k-uniform hypergraph on N vertices with codegree of size o(D/k log N) contains a matching that covers all but at most N((kC log N)/D)1/(2k−1+o(1)) of its vertices. In this article, we give a simple proof of the original result of Rödl and improve Grable's result for hypergraphs with bounded codegrees. The proof of the second result is based on the bound of Alon, Kim, and Spencer on matchings in linear hypergraphs. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13: 335–347, 1998

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