We call a tree T is even if every pair of its leaves is joined by a path of even length. Jackson and Yoshimoto{jacksonspanning}~[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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Ai et al. (2024) studied this question.
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