On enumeration of spanning trees of complete multipartite graphs containing a fixed spanning forest
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917245479813120 |
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| author | Wang, Wei Ge, Jun |
| author_facet | Wang, Wei Ge, Jun |
| contents | We present a determinantal formula for the number of spanning trees of a complete multipartite graph containing a given spanning forest $F$. Our approach relies on the Generalized Matrix Determinant Lemma and Jacobi's formula for the derivative of a determinant. This work generalizes known results for complete bipartite graphs and offers an algebraic perspective on the problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03602 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On enumeration of spanning trees of complete multipartite graphs containing a fixed spanning forest Wang, Wei Ge, Jun Combinatorics 05C30, 05C50 We present a determinantal formula for the number of spanning trees of a complete multipartite graph containing a given spanning forest $F$. Our approach relies on the Generalized Matrix Determinant Lemma and Jacobi's formula for the derivative of a determinant. This work generalizes known results for complete bipartite graphs and offers an algebraic perspective on the problem. |
| title | On enumeration of spanning trees of complete multipartite graphs containing a fixed spanning forest |
| topic | Combinatorics 05C30, 05C50 |
| url | https://arxiv.org/abs/2602.03602 |