New formulations of the union-closed sets conjecture
The union-closed sets conjecture states that if a finite set $\mathcal A$ of finite sets is union-closed and $\mathcal A\neq \{ \varnothing\}$, then there exists an element in $\displaystyle\cup_{A\in \mathcal A} A$ that belongs to at least half of the sets in $\mathcal A$. We present three new fo...
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| Language: | English |
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American Journal of Combinatorics
2022-02-01
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| Series: | The American Journal of Combinatorics |
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| Online Access: | https://ajcombinatorics.org/Volume1/V1.03.pdf |
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| _version_ | 1850123586465955840 |
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| author | Sudipta Mallik |
| author_facet | Sudipta Mallik |
| author_sort | Sudipta Mallik |
| collection | DOAJ |
| description | The union-closed sets conjecture states that if a finite set $\mathcal A$ of finite sets is union-closed and $\mathcal A\neq \{ \varnothing\}$, then there exists an element in $\displaystyle\cup_{A\in \mathcal A} A$ that belongs to at least half of the sets in $\mathcal A$. We present three new formulations of the union-closed conjecture in terms of matrices, graphs, and hypergraphs. |
| format | Article |
| id | doaj-art-099d1744f1da43bb861f79df0b0306bd |
| institution | OA Journals |
| issn | 2768-4202 |
| language | English |
| publishDate | 2022-02-01 |
| publisher | American Journal of Combinatorics |
| record_format | Article |
| series | The American Journal of Combinatorics |
| spelling | doaj-art-099d1744f1da43bb861f79df0b0306bd2025-08-20T02:34:33ZengAmerican Journal of CombinatoricsThe American Journal of Combinatorics2768-42022022-02-0114046New formulations of the union-closed sets conjectureSudipta Mallik0https://orcid.org/0000-0001-7496-2147Northern Arizona UniversityThe union-closed sets conjecture states that if a finite set $\mathcal A$ of finite sets is union-closed and $\mathcal A\neq \{ \varnothing\}$, then there exists an element in $\displaystyle\cup_{A\in \mathcal A} A$ that belongs to at least half of the sets in $\mathcal A$. We present three new formulations of the union-closed conjecture in terms of matrices, graphs, and hypergraphs.https://ajcombinatorics.org/Volume1/V1.03.pdfunion-closed sets conjecturegraphmatrixhypergraph |
| spellingShingle | Sudipta Mallik New formulations of the union-closed sets conjecture The American Journal of Combinatorics union-closed sets conjecture graph matrix hypergraph |
| title | New formulations of the union-closed sets conjecture |
| title_full | New formulations of the union-closed sets conjecture |
| title_fullStr | New formulations of the union-closed sets conjecture |
| title_full_unstemmed | New formulations of the union-closed sets conjecture |
| title_short | New formulations of the union-closed sets conjecture |
| title_sort | new formulations of the union closed sets conjecture |
| topic | union-closed sets conjecture graph matrix hypergraph |
| url | https://ajcombinatorics.org/Volume1/V1.03.pdf |
| work_keys_str_mv | AT sudiptamallik newformulationsoftheunionclosedsetsconjecture |