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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.07056 |
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| _version_ | 1866914945689452544 |
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| author | Ai, Jiangdong Gao, Zhipeng Liu, Xiangzhou Yue, Jun |
| author_facet | Ai, Jiangdong Gao, Zhipeng Liu, Xiangzhou Yue, Jun |
| contents | We call a tree $T$ is \emph{even} if every pair of its leaves is joined by a path of even length. Jackson and Yoshimoto~[J. Graph Theory, 2024] conjectured that every $r$-regular nonbipartite connected graph $G$ has a spanning even tree. They verified this conjecture for the case when $G$ has a $2$-factor. In this paper, we prove that the conjecture holds when $r$ is odd, thereby resolving the only remaining unsolved case for this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07056 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A short note on spanning even trees Ai, Jiangdong Gao, Zhipeng Liu, Xiangzhou Yue, Jun Combinatorics We call a tree $T$ is \emph{even} if every pair of its leaves is joined by a path of even length. Jackson and Yoshimoto~[J. Graph Theory, 2024] conjectured that every $r$-regular nonbipartite connected graph $G$ has a spanning even tree. They verified this conjecture for the case when $G$ has a $2$-factor. In this paper, we prove that the conjecture holds when $r$ is odd, thereby resolving the only remaining unsolved case for this conjecture. |
| title | A short note on spanning even trees |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.07056 |