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arXiv · 2408.07056

A short note on spanning even trees

Jiangdong Ai·Zhipeng Gao·Xiangzhou Liu·Jun Yue
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Abstract

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.

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Jiangdong Ai, Zhipeng Gao, Xiangzhou Liu, Jun Yue. 2024-09-10. A short note on spanning even trees. https://arxiv.org/abs/2408.07056

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