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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.23932 |
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| _version_ | 1866910679326261248 |
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| author | Freij-Hollanti, Ragnar Šapokaitė, Patricija |
| author_facet | Freij-Hollanti, Ragnar Šapokaitė, Patricija |
| contents | We propose a novel definition of hypergraphical matroids, defined for arbitrary hypergraphs, simultaneously generalizing previous definitions for regular hypergraphs (Main, 1978), and for the hypergraphs of circuits of a matroid (Freij-Hollanti, Jurrius, Kuznetsova, 2023). As a consequence, we obtain a new notion of cycles in hypergraphs, and hypertrees. We give an equivalence relation on hypergraphs, according to when their so-called matroidal closures agree. Finally, we characterize hypergraphs that are isomorphic to the circuit hypergraphs of the associated matroids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23932 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Matroidal Cycles and Hypergraph Families Freij-Hollanti, Ragnar Šapokaitė, Patricija Combinatorics We propose a novel definition of hypergraphical matroids, defined for arbitrary hypergraphs, simultaneously generalizing previous definitions for regular hypergraphs (Main, 1978), and for the hypergraphs of circuits of a matroid (Freij-Hollanti, Jurrius, Kuznetsova, 2023). As a consequence, we obtain a new notion of cycles in hypergraphs, and hypertrees. We give an equivalence relation on hypergraphs, according to when their so-called matroidal closures agree. Finally, we characterize hypergraphs that are isomorphic to the circuit hypergraphs of the associated matroids. |
| title | Matroidal Cycles and Hypergraph Families |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.23932 |