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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.03735 |
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| _version_ | 1866913429139226624 |
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| author | Aharoni, Ron Berger, Eli Briggs, Joseph Guo, He Zerbib, Shira |
| author_facet | Aharoni, Ron Berger, Eli Briggs, Joseph Guo, He Zerbib, Shira |
| contents | A pair $(A,B)$ of hypergraphs is called orthogonal if $|a \cap b|=1$ for every pair of edges $a \in A$ and $b \in B$. An orthogonal pair of hypergraphs is called a loom if each of its two members is the set of minimum covers of the other. Looms appear naturally in the context of a conjecture of Gyárfás and Lehel on the covering number of cross-intersecting hypergraphs. We study their properties and ways of construction, and prove special cases of a conjecture that if true would imply the Gyárfás--Lehel conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03735 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Looms Aharoni, Ron Berger, Eli Briggs, Joseph Guo, He Zerbib, Shira Combinatorics Discrete Mathematics 05C65, 05C35, 05C72, 05C76, 05D15 A pair $(A,B)$ of hypergraphs is called orthogonal if $|a \cap b|=1$ for every pair of edges $a \in A$ and $b \in B$. An orthogonal pair of hypergraphs is called a loom if each of its two members is the set of minimum covers of the other. Looms appear naturally in the context of a conjecture of Gyárfás and Lehel on the covering number of cross-intersecting hypergraphs. We study their properties and ways of construction, and prove special cases of a conjecture that if true would imply the Gyárfás--Lehel conjecture. |
| title | Looms |
| topic | Combinatorics Discrete Mathematics 05C65, 05C35, 05C72, 05C76, 05D15 |
| url | https://arxiv.org/abs/2309.03735 |