A short note on spanning even trees
Combinatorics
2024-09-11 v2
Abstract
We call a tree 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 -regular nonbipartite connected graph has a spanning even tree. They verified this conjecture for the case when has a -factor. In this paper, we prove that the conjecture holds when is odd, thereby resolving the only remaining unsolved case for this conjecture.
Keywords
Cite
@article{arxiv.2408.07056,
title = {A short note on spanning even trees},
author = {Jiangdong Ai and Zhipeng Gao and Xiangzhou Liu and Jun Yue},
journal= {arXiv preprint arXiv:2408.07056},
year = {2024}
}
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6 pages