Combinatorica

, Volume 21, Issue 1, pp 89–94

The Clique Complex and Hypergraph Matching

  • Roy Meshulam
Original Paper

DOI: 10.1007/s004930170006

Cite this article as:
Meshulam, R. Combinatorica (2001) 21: 89. doi:10.1007/s004930170006

The width of a hypergraph \(\) is the minimal \(\) for which there exist \(\) such that for any \(\), \(\) for some \(\). The matching width of \(\) is the minimal \(\) such that for any matching \(\) there exist \(\) such that for any \(\), \(\) for some \(\). The following extension of the Aharoni-Haxell matching Theorem [3] is proved: Let \(\) be a family of hypergraphs such that for each \(\) either \(\) or \(\), then there exists a matching \(\) such that \(\) for all \(\). This is a consequence of a more general result on colored cliques in graphs. The proofs are topological and use the Nerve Theorem.

AMS Subject Classification (1991) Classes:  05D05, 05D15, 05E25

Copyright information

© János Bolyai Mathematical Society, 2001

Authors and Affiliations

  • Roy Meshulam
    • 1
  1. 1.Department of Mathematics, Technion; Haifa 32000, Israel; E-mail: meshulam@math.technion.ac.ilIL