{
  "id": "2004.05433",
  "version": "v1",
  "published": "2020-04-11T16:02:21.000Z",
  "updated": "2020-04-11T16:02:21.000Z",
  "title": "Clique immersions in graphs with certain forbidden subgraphs",
  "authors": [
    "Daniel A. Quiroz"
  ],
  "comment": "13 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Lescure-Meyniel conjecture is the analogue of Hadwiger's conjecture for the immersion order. It states that every graph $G$ contains the complete graph $K_{\\chi(G)}$ as an immersion, and like its minor-order counterpart it is open even for graphs with independence number 2. We show that every graph $G$ with independence number $\\alpha(G)\\ge 2$ and no hole of length between $4$ and $2\\alpha(G)$ satisfies this conjecture. In particular, every $C_4$-free graph $G$ with $\\alpha(G)= 2$ satisfies the Lescure-Meyniel conjecture. We give another generalisation of this corollary, as follows. Let $G$ and $H$ be graphs with independence number at most 2, such that $|V(H)|\\le 4$. If $G$ is $H$-free, then $G$ satisfies the Lescure-Meyniel conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-11T16:02:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C69"
    ],
    "keywords": [
      "forbidden subgraphs",
      "clique immersions",
      "independence number",
      "lescure-meyniel conjecture",
      "immersion order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}