The two-variable hypergraph Tutte polynomial via embedding activities
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929459602391040 |
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| author | Tóthmérész, Lilla |
| author_facet | Tóthmérész, Lilla |
| contents | We prove that the two-variable Tutte polynomial of hypergraphs can be defined via embedding activities. We also prove that embedding activities of hypergraphs yield a Crapo-style decomposition of $\mathbb{Z}^E$, thus generalizing Bernardi's results from graphs to hypergraphs.
We also show that hypergraph embedding activities do not fit into the $Δ$-activity framework of Courtiel. Based on this observation, we construct a graph with an activity notion that yields a Crapo decomposition, but cannot be obtained as a $Δ$-activity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_20639 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The two-variable hypergraph Tutte polynomial via embedding activities Tóthmérész, Lilla Combinatorics 05C31, 05C65, 52B40 We prove that the two-variable Tutte polynomial of hypergraphs can be defined via embedding activities. We also prove that embedding activities of hypergraphs yield a Crapo-style decomposition of $\mathbb{Z}^E$, thus generalizing Bernardi's results from graphs to hypergraphs. We also show that hypergraph embedding activities do not fit into the $Δ$-activity framework of Courtiel. Based on this observation, we construct a graph with an activity notion that yields a Crapo decomposition, but cannot be obtained as a $Δ$-activity. |
| title | The two-variable hypergraph Tutte polynomial via embedding activities |
| topic | Combinatorics 05C31, 05C65, 52B40 |
| url | https://arxiv.org/abs/2310.20639 |