Transversals in Uniform Hypergraphs with Property (p,2)

Dedicated to the memory of Paul Erdős

Let f(r,p,t) (p > t >= 1, r >= 2) be the maximum of the cardinality of a minimum transversal over all r-uniform hypergraphs possessing the property that every subhypergraph of with p edges has a transversal of size t. The values of f(r,p,2) for p = 3, 4, 5, 6 were found in [1] and bounds on f(r,7,2) are given in [3]. Here we prove that for large p and huge r.

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Received September 23, 1999


ID="*" This work was partially supported by the grant 99-01-00581 of the Russian Foundation for Fundamental Research and the Dutch–Russian Grant NWO-047-008-006.

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V. Kostochka, A. Transversals in Uniform Hypergraphs with Property (p,2). Combinatorica 22, 275–285 (2002).

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  • AMS Subject Classification (2000) Classes:  05C65