Asymptotic Enumeration of Non-Uniform Linear Hypergraphs
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 prov...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2022-02-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.2246 |
| _version_ | 1827840361883500544 |
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| author | Hasheminezhad Mahdieh McKay Brendan D. |
| author_facet | Hasheminezhad Mahdieh McKay Brendan D. |
| author_sort | Hasheminezhad Mahdieh |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T07:32:42Z |
| format | Article |
| id | doaj.art-d6f8eb130f44408cba431c27229a8e25 |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T07:32:42Z |
| publishDate | 2022-02-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-d6f8eb130f44408cba431c27229a8e252023-09-02T21:43:01ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922022-02-0142121923010.7151/dmgt.2246Asymptotic Enumeration of Non-Uniform Linear HypergraphsHasheminezhad Mahdieh0McKay Brendan D.1Department of Computer Science, Yazd University, Yazd, Iran, Combinatorial and Geometric Algorithms LabResearch School of Computer Science, Australian National University, Canberra, ACT 2601, AustraliaA 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.https://doi.org/10.7151/dmgt.2246steiner systemlinear hypergraphasymptotic enumerationswitching method05a1605c65 |
| spellingShingle | Hasheminezhad Mahdieh McKay Brendan D. Asymptotic Enumeration of Non-Uniform Linear Hypergraphs Discussiones Mathematicae Graph Theory steiner system linear hypergraph asymptotic enumeration switching method 05a16 05c65 |
| title | Asymptotic Enumeration of Non-Uniform Linear Hypergraphs |
| title_full | Asymptotic Enumeration of Non-Uniform Linear Hypergraphs |
| title_fullStr | Asymptotic Enumeration of Non-Uniform Linear Hypergraphs |
| title_full_unstemmed | Asymptotic Enumeration of Non-Uniform Linear Hypergraphs |
| title_short | Asymptotic Enumeration of Non-Uniform Linear Hypergraphs |
| title_sort | asymptotic enumeration of non uniform linear hypergraphs |
| topic | steiner system linear hypergraph asymptotic enumeration switching method 05a16 05c65 |
| url | https://doi.org/10.7151/dmgt.2246 |
| work_keys_str_mv | AT hasheminezhadmahdieh asymptoticenumerationofnonuniformlinearhypergraphs AT mckaybrendand asymptoticenumerationofnonuniformlinearhypergraphs |