The enumeration of odd spanning trees in graphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866911433617309696 |
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| author | Xu, Shaohan Xu, Kexiang |
| author_facet | Xu, Shaohan Xu, Kexiang |
| contents | A graph is odd if all of its vertices have odd degrees. In particular, an odd spanning tree in a connected graph is a spanning tree in which all vertices have odd degrees. In this paper we establish a unified technique to enumerate odd spanning trees of a graph $G$ in terms of a multivariable polynomial associated with $G$ and indeterminates $\{x_{i}:v_i\in V(G)\}$. As applications, the enumerative formulas for odd spanning trees in complete graphs, complete multipartite graphs, almost complete graphs, complete split graphs and Ferrers graphs are, respectively, derived from our work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08179 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The enumeration of odd spanning trees in graphs Xu, Shaohan Xu, Kexiang Combinatorics A graph is odd if all of its vertices have odd degrees. In particular, an odd spanning tree in a connected graph is a spanning tree in which all vertices have odd degrees. In this paper we establish a unified technique to enumerate odd spanning trees of a graph $G$ in terms of a multivariable polynomial associated with $G$ and indeterminates $\{x_{i}:v_i\in V(G)\}$. As applications, the enumerative formulas for odd spanning trees in complete graphs, complete multipartite graphs, almost complete graphs, complete split graphs and Ferrers graphs are, respectively, derived from our work. |
| title | The enumeration of odd spanning trees in graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.08179 |