2024/08/13 by Jiangdong Ai, Zhipeng Gao, Ai, Jiangdong +4
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2408.07056
openalex publication_date 2024/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We call a tree T is 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.