Degree Sequences vs. Forests in Bipartite Graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915828958494720 |
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| author | Grinberg, Darij Liber, Benjamin |
| author_facet | Grinberg, Darij Liber, Benjamin |
| contents | We prove a conjecture of Shteiner and Shteyner stating that for a bipartite graph $G=(V,E)$, the number of forests in $G$ equals the number of degree sequences arising from its spanning subgraphs. In the process, we provide several equivalent evaluations of the Tutte polynomial $T_G(x,y)$ at $(2,1)$, including interpretations in terms of degree vectors obtained from orientations of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02151 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Degree Sequences vs. Forests in Bipartite Graphs Grinberg, Darij Liber, Benjamin Combinatorics 05C31 We prove a conjecture of Shteiner and Shteyner stating that for a bipartite graph $G=(V,E)$, the number of forests in $G$ equals the number of degree sequences arising from its spanning subgraphs. In the process, we provide several equivalent evaluations of the Tutte polynomial $T_G(x,y)$ at $(2,1)$, including interpretations in terms of degree vectors obtained from orientations of $G$. |
| title | Degree Sequences vs. Forests in Bipartite Graphs |
| topic | Combinatorics 05C31 |
| url | https://arxiv.org/abs/2603.02151 |