The number of hypergraphs and colored Hypergraphs with hereditary properties

Abstract

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.

9 pages

References in corpus (7)

• Hypergraph regularity and the multidimensional Szemerédi theorem
• Limits of Hypergraphs, Removal and Regularity Lemmas. A Non-standard Approach
• A Simple Regularization of Hypergraphs
• Linear Ramsey numbers for bounded-degree hypergraphs
• Embeddings and Ramsey numbers of sparse k-uniform hypergraphs
• Removal lemma for infinitely-many forbidden hypergraphs and property testing
• 3-Uniform hypergraphs of bounded degree have linear Ramsey numbers

Cited by in corpus (3)

• Overview of some general results in combinatorial enumeration
• Multicolour containers and the entropy of decorated graph limits
• The structure of almost all graphs in a hereditary property