Asymptotic enumeration of hypergraphs by degree sequence

Nina Kamcev; Anita Liebenau; Nicholas Wormald

doi:10.19086/aic.32357

Asymptotic enumeration of hypergraphs by degree sequence

Nina Kamcev
, Anita Liebenau
, Nicholas Wormald

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

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 verticesprovided that dn ≤ c nk 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.

Original language	English
Article number	1
Number of pages	36
Journal	Advances in Combinatorics
Volume	2022
DOIs	https://doi.org/10.19086/aic.32357
Publication status	Published - 3 Feb 2022

Access to Document

10.19086/aic.32357Licence: CC BY

Cite this

@article{8aadb27d0c0a48e89b661fac6eced2f8,

title = "Asymptotic enumeration of hypergraphs by degree sequence",

abstract = "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 verticesprovided that dn ≤ c nk 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.",

author = "Nina Kamcev and Anita Liebenau and Nicholas Wormald",

year = "2022",

month = feb,

day = "3",

doi = "10.19086/aic.32357",

language = "English",

volume = "2022",

journal = "Advances in Combinatorics",

issn = "2517-5599",

publisher = "Alliance of Diamond Open Access Journals",

}

TY - JOUR

T1 - Asymptotic enumeration of hypergraphs by degree sequence

AU - Kamcev, Nina

AU - Liebenau, Anita

AU - Wormald, Nicholas

PY - 2022/2/3

Y1 - 2022/2/3

N2 - 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 verticesprovided that dn ≤ c nk 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.

AB - 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 verticesprovided that dn ≤ c nk 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.

U2 - 10.19086/aic.32357

DO - 10.19086/aic.32357

M3 - Article

SN - 2517-5599

VL - 2022

JO - Advances in Combinatorics

JF - Advances in Combinatorics

M1 - 1

ER -