{
  "id": "2408.07056",
  "version": "v1",
  "published": "2024-08-13T17:48:42.000Z",
  "updated": "2024-08-13T17:48:42.000Z",
  "title": "A short note on spanning even trees",
  "authors": [
    "Jiangdong Ai",
    "Zhipeng Gao",
    "Xiangzhou Liu"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO"
  ],
  "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\\cite{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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-13T17:48:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "short note",
      "regular nonbipartite connected graph",
      "conjecture holds",
      "graph theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}