Asymptotic enumeration of sparse uniform hypergraphs with given degrees

Abstract

Let $r\ge 2$ be a fixed integer. For infinitely many $n$, let $\mathbf{k}=(k_1,...,k_n)$ be a vector of nonnegative integers such that their sum $M$ is divisible by $r$. We present an asymptotic enumeration formula for simple $r$-uniform hypergraphs with degree sequence $k$. (Here "simple" means that all edges are distinct and no edge contains a repeated vertex.) Our formula holds whenever the maximum degree $k_{\max }$ satisfies $k_{\max }^3=o(M)$.

15 pages, 1 figure. Revised to take into account referee's comments

References in corpus (2)

• Random hypergraphs and their applications
• Approximate counting of regular hypergraphs

Cited by in corpus (4)

• Approximate counting of regular hypergraphs
• Asymptotic enumeration of hypergraphs by degree sequence
• Asymptotic enumeration of linear hypergraphs with given number of vertices and edges
• On the number of linear multipartite hypergraphs with given size