The Clique Complex and Hypergraph Matching

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.

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Received June 14, 1999

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Meshulam, R. The Clique Complex and Hypergraph Matching. Combinatorica 21, 89–94 (2001). https://doi.org/10.1007/s004930170006

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