A new strategy for finding spanning trees without small degree stems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910984115847168 |
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| author | Furuya, Michitaka Tsuchiya, Shoichi |
| author_facet | Furuya, Michitaka Tsuchiya, Shoichi |
| contents | For an integer $k\geq 2$, a spanning tree of a graph without vertices of degree from $2$ to $k$ is called a {\it $[2,k]$-ST} of the graph. The concept of $[2,k]$-STs is a natural extension of a homeomorphically irreducible spanning tree (or HIST), which is a well-studied graph structure. In this paper, we give a new strategy for finding $[2,k]$-STs. By using the strategy, we refine or extend a known degree-sum condition for the existence of a HIST. Furthermore, we also investigate a degree-product condition for the existence of a $[2,k]$-ST. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03762 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A new strategy for finding spanning trees without small degree stems Furuya, Michitaka Tsuchiya, Shoichi Combinatorics 05C05, 05C07 For an integer $k\geq 2$, a spanning tree of a graph without vertices of degree from $2$ to $k$ is called a {\it $[2,k]$-ST} of the graph. The concept of $[2,k]$-STs is a natural extension of a homeomorphically irreducible spanning tree (or HIST), which is a well-studied graph structure. In this paper, we give a new strategy for finding $[2,k]$-STs. By using the strategy, we refine or extend a known degree-sum condition for the existence of a HIST. Furthermore, we also investigate a degree-product condition for the existence of a $[2,k]$-ST. |
| title | A new strategy for finding spanning trees without small degree stems |
| topic | Combinatorics 05C05, 05C07 |
| url | https://arxiv.org/abs/2303.03762 |