Asymptotic Enumeration of Hypergraphs by Degree Sequence
Copyright policy )Asymptotic Enumeration of Hypergraphs by Degree Sequence
We prove an asymptotic formula for the number of k-uniform hypergraphs with a given degree sequence, for a wide range of parameters. In particular, we find a formula that is asymptotically equal to the number of d-regular k-uniform hypergraphs on n vertices provided that dn ≤ c(n/k) for a constant c > 0, and 3 ≤ k < n^c for any C < 1/9. Our results relate the degree sequence of a random k-uniform hypergraph to a simple model of nearly independent binomial random variables, thus extending the recent results for graphs due to the second and third author.
- University of Zagreb Croatia
- Monash University Australia
- UNSW Sydney Australia
degree sequence, asymptotic enumeration, hypergraph, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05A16, 05C30, 05C65, Enumeration in graph theory, Hypergraphs, Asymptotic enumeration
degree sequence, asymptotic enumeration, hypergraph, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05A16, 05C30, 05C65, Enumeration in graph theory, Hypergraphs, Asymptotic enumeration
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