# The Clique Complex and Hypergraph Matching

Original Paper

DOI: 10.1007/s004930170006

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

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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

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© János Bolyai Mathematical Society, 2001