Refinements of degree conditions for the existence of a spanning tree without small degree stems
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929453336100864 |
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| author | Furuya, Michitaka Saito, Akira Tsuchiya, Shoichi |
| author_facet | Furuya, Michitaka Saito, Akira Tsuchiya, Shoichi |
| contents | A spanning tree of a graph without no vertices of degree $2$ is called a {\it homeomorphically irreducible spanning tree} (or a {\it HIST}) of the graph. Albertson, Berman, Hutchinson and Thomassen~[J. Graph Theory {\bf 14} (1990), 247--258] gave a minimum degree condition for the existence of a HIST, and recently, Ito and Tsuchiya~[J. Graph Theory {\bf 99} (2022), 162--170] found a sharp degree-sum condition for the existence of a HIST. In this paper, we refine these results, and extend the first one to a spanning tree in which no vertex other than the endvertices has small degree. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_02372 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Refinements of degree conditions for the existence of a spanning tree without small degree stems Furuya, Michitaka Saito, Akira Tsuchiya, Shoichi Combinatorics 05C05, 05C07 A spanning tree of a graph without no vertices of degree $2$ is called a {\it homeomorphically irreducible spanning tree} (or a {\it HIST}) of the graph. Albertson, Berman, Hutchinson and Thomassen~[J. Graph Theory {\bf 14} (1990), 247--258] gave a minimum degree condition for the existence of a HIST, and recently, Ito and Tsuchiya~[J. Graph Theory {\bf 99} (2022), 162--170] found a sharp degree-sum condition for the existence of a HIST. In this paper, we refine these results, and extend the first one to a spanning tree in which no vertex other than the endvertices has small degree. |
| title | Refinements of degree conditions for the existence of a spanning tree without small degree stems |
| topic | Combinatorics 05C05, 05C07 |
| url | https://arxiv.org/abs/2303.02372 |