Abstract
AbstractMorris and Saxton used the method of containers to bound the number of ‐vertex graphs with edges containing no ‐cycles, and hence graphs of girth more than . We consider a generalization to ‐uniform hypergraphs. The girth of a hypergraph is the minimum such that there exist distinct vertices and hyperedges with for all . Letting denote the number of ‐vertex ‐uniform hypergraphs with edges and girth larger than and defining , we show which is tight when divides up to a term in the exponent. This result is used to address the extremal problem for subgraphs of girth more than in random ‐uniform hypergraphs.
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