The number of hypergraphs and colored Hypergraphs with hereditary properties

Details The number of hypergraphs and colored Hypergraphs with hereditary properties The number of hypergraphs and colored Hypergraphs with hereditary properties

2007-12-04

arxiv.org/abs/0712.0425v1

Mathematics

Combinatorics

9 pages

Scientific paper

As an application of Szemeredi's regularity lemma, Erdos-Frankl-Rodl (1986) showed that the number of graphs on vertex set {1,2,...n} with a monotone class P is $2^{(1+o(1))ex(n,P)n^2/2}$ where $ex(n,P)$ is the maximum number of edges of an n-vertex graph which has no subgraph in P. Kohayakawa et al. (2003) extended it from monotone to hereditary and from graphs to 3-uniform hypergraphs. We extend it to general hypergraphs. This may be a simple example illustrating how to apply a recent hypergraph regularity lemma by the author.

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