{
  "id": "2305.05713",
  "version": "v1",
  "published": "2023-05-09T18:46:02.000Z",
  "updated": "2023-05-09T18:46:02.000Z",
  "title": "On density conditions for transversal trees in multipartite graphs",
  "authors": [
    "Leila Badakhshian",
    "Victor Falgas-Ravry",
    "Maryam Sharifzadeh"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be an $r$-partite graph such that the edge density between any two parts is at least $\\alpha$. How large does $\\alpha$ need to be to guarantee that $G$ contains a connected transversal, that is, a tree on $r$ vertices meeting each part in one vertex? And what if instead we want to guarantee the existence of a Hamiltonian transversal? In this paper we initiate the study of such extremal multipartite graph problems, obtaining a number of results and providing many new constructions, conjectures and further questions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-09T18:46:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "transversal trees",
      "density conditions",
      "extremal multipartite graph problems",
      "edge density",
      "hamiltonian transversal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}