{
  "id": "2409.15522",
  "version": "v1",
  "published": "2024-09-23T20:16:44.000Z",
  "updated": "2024-09-23T20:16:44.000Z",
  "title": "Spanning weakly even trees of graphs",
  "authors": [
    "M. N. Ellingham",
    "Yixuan Huang",
    "Songling Shan",
    "Simon Špacapan"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a graph (with multiple edges allowed) and let $T$ be a tree in $G$. We say that $T$ is $\\textit{even}$ if every leaf of $T$ belongs to the same part of the bipartition of $T$, and that $T$ is $\\textit{weakly even}$ if every leaf of $T$ that has maximum degree in $G$ belongs to the same part of the bipartition of $T$. We confirm two recent conjectures of Jackson and Yoshimoto by showing that every connected graph that is not a regular bipartite graph has a spanning weakly even tree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-23T20:16:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C05",
      "05C07"
    ],
    "keywords": [
      "regular bipartite graph",
      "bipartition",
      "multiple edges",
      "maximum degree",
      "conjectures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}