English

A short note on spanning even trees

Combinatorics 2024-09-11 v2

Abstract

We call a tree TT 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 rr-regular nonbipartite connected graph GG has a spanning even tree. They verified this conjecture for the case when GG has a 22-factor. In this paper, we prove that the conjecture holds when rr 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}
}

Comments

6 pages

R2 v1 2026-06-28T18:12:02.927Z