The enumeration of odd spanning trees in graphs

Fuente: arXiv
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Autori principali: Xu, Shaohan, Xu, Kexiang
Natura: Preprint
Pubblicazione: 2026
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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