Spectral radius and homeomorphically irreducible spanning trees of graphs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909766039633920 |
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| author | Gao, Bingqian Liu, Huiqing Zhao, Jing |
| author_facet | Gao, Bingqian Liu, Huiqing Zhao, Jing |
| contents | For a connected graph $G$, a spanning tree $T$ of $G$ is called a homeomorphically irreducible spanning tree (HIST) if $T$ has no vertices of degree 2. Albertson {\em et al.} proved that it is $NP$-complete to decide whether a graph contains a HIST. In this paper, we provide some spectral conditions that guarantee the existence of a HIST in a connected graph. Furthermore, we also present some sufficient conditions in terms of the order of a graph $G$ to ensure the existence of a HIST in $G$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_02021 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral radius and homeomorphically irreducible spanning trees of graphs Gao, Bingqian Liu, Huiqing Zhao, Jing Combinatorics 05C35, 05C50 For a connected graph $G$, a spanning tree $T$ of $G$ is called a homeomorphically irreducible spanning tree (HIST) if $T$ has no vertices of degree 2. Albertson {\em et al.} proved that it is $NP$-complete to decide whether a graph contains a HIST. In this paper, we provide some spectral conditions that guarantee the existence of a HIST in a connected graph. Furthermore, we also present some sufficient conditions in terms of the order of a graph $G$ to ensure the existence of a HIST in $G$. |
| title | Spectral radius and homeomorphically irreducible spanning trees of graphs |
| topic | Combinatorics 05C35, 05C50 |
| url | https://arxiv.org/abs/2509.02021 |