The Minimum Size of Saturated Hypergraphs

Authors:
Oleg Pikhurko
Affiliations:
Department of Pure Mathematics and Mathematical Statistics, Cambridge University, Cambridge CB2 1SB, England (e-mail: O.Pikhurko@dpmms.cam.ac.uk)
Venue:
Combinatorics, Probability and Computing
Year:
1999

Citing 3
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Abstract

Let ℱ be a family of forbidden k-hypergraphs (k-uniform set systems). An ℱ-saturated hypergraph is a maximal k-uniform set system not containing any member of ℱ. As the main result we prove that, for any finite family ℱ, the minimum number of edges of an ℱ-saturated hypergraph is O(nk−1). In particular, this implies a conjecture of Tuza. Some other related results are presented.