DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

Article in press


Authors:

M. Hasheminezhad, B.D. McKay

Title:

Asymptotic enumeration of non-uniform linear hypergraphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2019-01-12, Revised: 2019-09-21, Accepted: 2019-09-21, https://doi.org/10.7151/dmgt.2246

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.

Keywords:

Steiner system, linear hypergraph, asymptotic enumeration, switching method

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