Asymptotic Enumeration of Non-Uniform Linear Hypergraphs

Mahdieh Hasheminezhad; Brendan D. McKay

doi:10.7151/dmgt.2246

Asymptotic Enumeration of Non-Uniform Linear Hypergraphs

Mahdieh Hasheminezhad, Brendan D. McKay

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Abstract

A linear hypergraph, also known as a partial Steiner system, is a collection of subsets of a set such that no two of the subsets have more than one element in common. Most studies of linear hypergraphs consider only the uniform case, in which all the subsets have the same size. In this paper we provide, for the first time, asymptotically precise estimates of the number of linear hypergraphs in the non-uniform case, as a function of the number of subsets of each size.

Original language	English
Journal	Discussiones Mathematicae - Graph Theory
DOIs	https://doi.org/10.7151/dmgt.2246
Publication status	Published - 2019

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abstract = "A linear hypergraph, also known as a partial Steiner system, is a collection of subsets of a set such that no two of the subsets have more than one element in common. Most studies of linear hypergraphs consider only the uniform case, in which all the subsets have the same size. In this paper we provide, for the first time, asymptotically precise estimates of the number of linear hypergraphs in the non-uniform case, as a function of the number of subsets of each size.",

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AB - A linear hypergraph, also known as a partial Steiner system, is a collection of subsets of a set such that no two of the subsets have more than one element in common. Most studies of linear hypergraphs consider only the uniform case, in which all the subsets have the same size. In this paper we provide, for the first time, asymptotically precise estimates of the number of linear hypergraphs in the non-uniform case, as a function of the number of subsets of each size.

KW - Steiner system

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KW - linear hypergraph

KW - switching method

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JO - Discussiones Mathematicae - Graph Theory

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Asymptotic Enumeration of Non-Uniform Linear Hypergraphs

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