A closure result on spanning $k$-trees of graphs with given minimum degree
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917436270313472 |
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| author | Zhang, Wenqian |
| author_facet | Zhang, Wenqian |
| contents | Let $k\geq2$ be an integer. A $k$-tree is a tree with maximum degree at most $k$. In this paper, we give a closure result on spanning $k$-trees of graphs with given minimum degree. Let $δ\geq1$ be an integer, and $G$ be a connected graph of order $n$ with minimum degree $δ$. Let $u$ and $v$ be two nonadjacent vertices of $G$ satisfying $d_{G}(u)+d_{G}(v)\geq n-1-(k-2)δ$. Then $G$ has a spanning $k$-tree if and only if $G+uv$ has a spanning $k$-tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17728 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A closure result on spanning $k$-trees of graphs with given minimum degree Zhang, Wenqian Combinatorics Let $k\geq2$ be an integer. A $k$-tree is a tree with maximum degree at most $k$. In this paper, we give a closure result on spanning $k$-trees of graphs with given minimum degree. Let $δ\geq1$ be an integer, and $G$ be a connected graph of order $n$ with minimum degree $δ$. Let $u$ and $v$ be two nonadjacent vertices of $G$ satisfying $d_{G}(u)+d_{G}(v)\geq n-1-(k-2)δ$. Then $G$ has a spanning $k$-tree if and only if $G+uv$ has a spanning $k$-tree. |
| title | A closure result on spanning $k$-trees of graphs with given minimum degree |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.17728 |