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The Minimum Size of Saturated Hypergraphs

Published online by Cambridge University Press:  01 September 1999

OLEG PIKHURKO
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Cambridge University, Cambridge CB2 1SB, England (e-mail: O.Pikhurko@dpmms.cam.ac.uk)

Abstract

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

Type
Research Article
Copyright
1999 Cambridge University Press

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