Hypergraphs with vanishing Turán density in uniformly dense hypergraphs

Abstract

Erdős [Israel J. Math. 2 (1964) 183–190] characterised those hypergraphs F that have to appear in any sufficiently large hypergraph H of positive density. We study related questions for 3-uniform hypergraphs with the additional assumption that H has to be uniformly dense with respect to vertex sets. In particular, we characterise those hypergraphs F that are guaranteed to appear in large uniformly dense hypergraphs H of positive density. We also review the case when the density of the induced subhypergraphs of H may depend on the proportion of the considered vertex sets.

Locations

• Journal of the London Mathematical Society - View
• arXiv (Cornell University) - View - PDF
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