A neighborhood union condition for the existence of a spanning tree without samll degree vertices
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909832323268608 |
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| author | Li, Yibo Dong, Fengming Liu, Huiqing |
| author_facet | Li, Yibo Dong, Fengming Liu, Huiqing |
| contents | For an integer k\ge2, a [2,k]-ST of a connected graph G is a spanning tree of G in which there are no vertices of degree between 2 and k. A [2,k]-ST is a natural extension of a homeomorphically irreducible spanning tree (HIST), which is a spanning tree without vertices of degree 2. In this paper, we give a neighborhood union condition for the existence of a [2,k]-ST in G. We generalize a known degree sum condition that guarantees the existence of a [2,k]-ST in G. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07655 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A neighborhood union condition for the existence of a spanning tree without samll degree vertices Li, Yibo Dong, Fengming Liu, Huiqing Combinatorics 05C05 For an integer k\ge2, a [2,k]-ST of a connected graph G is a spanning tree of G in which there are no vertices of degree between 2 and k. A [2,k]-ST is a natural extension of a homeomorphically irreducible spanning tree (HIST), which is a spanning tree without vertices of degree 2. In this paper, we give a neighborhood union condition for the existence of a [2,k]-ST in G. We generalize a known degree sum condition that guarantees the existence of a [2,k]-ST in G. |
| title | A neighborhood union condition for the existence of a spanning tree without samll degree vertices |
| topic | Combinatorics 05C05 |
| url | https://arxiv.org/abs/2510.07655 |