{
  "id": "1909.07964",
  "version": "v1",
  "published": "2019-09-17T17:53:41.000Z",
  "updated": "2019-09-17T17:53:41.000Z",
  "title": "On clique immersions in line graphs",
  "authors": [
    "Michael Guyer",
    "Jessica McDonald"
  ],
  "comment": "10 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that if $L(G)$ immerses $K_t$ then $L(mG)$ immerses $K_{mt}$, where $mG$ is the graph obtained from $G$ by replacing each edge in $G$ with a parallel edge of multiplicity $m$. This implies that when $G$ is a simple graph, $L(mG)$ satisfies a conjecture of Abu-Khzam and Langston. We also show that when $G$ is a line graph, $G$ has a $K_t$-immersion iff $G$ has a $K_t$-minor whenever $t\\leq 4$, but this equivalence fails in both directions when $t=5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-17T17:53:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "line graph",
      "clique immersions",
      "equivalence fails",
      "parallel edge",
      "simple graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}