Spanning weakly even trees of graphs
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arXiv
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| Autores principales: | , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913551319302144 |
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| author | Ai, Jiangdong Ellingham, M. N. Gao, Zhipeng Huang, Yixuan Liu, Xiangzhou Shan, Songling Špacapan, Simon Yue, Jun |
| author_facet | Ai, Jiangdong Ellingham, M. N. Gao, Zhipeng Huang, Yixuan Liu, Xiangzhou Shan, Songling Špacapan, Simon Yue, Jun |
| contents | Let $G$ be a graph (with multiple edges allowed) and let $T$ be a tree in $G$. We say that $T$ is $\textit{even}$ if every leaf of $T$ belongs to the same part of the bipartition of $T$, and that $T$ is $\textit{weakly even}$ if every leaf of $T$ that has maximum degree in $G$ belongs to the same part of the bipartition of $T$. We confirm two recent conjectures of Jackson and Yoshimoto by showing that every connected graph that is not a regular bipartite graph has a spanning weakly even tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15522 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spanning weakly even trees of graphs Ai, Jiangdong Ellingham, M. N. Gao, Zhipeng Huang, Yixuan Liu, Xiangzhou Shan, Songling Špacapan, Simon Yue, Jun Combinatorics 05C05 (Primary) 05C07 (Secondary) Let $G$ be a graph (with multiple edges allowed) and let $T$ be a tree in $G$. We say that $T$ is $\textit{even}$ if every leaf of $T$ belongs to the same part of the bipartition of $T$, and that $T$ is $\textit{weakly even}$ if every leaf of $T$ that has maximum degree in $G$ belongs to the same part of the bipartition of $T$. We confirm two recent conjectures of Jackson and Yoshimoto by showing that every connected graph that is not a regular bipartite graph has a spanning weakly even tree. |
| title | Spanning weakly even trees of graphs |
| topic | Combinatorics 05C05 (Primary) 05C07 (Secondary) |
| url | https://arxiv.org/abs/2409.15522 |