{
  "id": "1508.05378",
  "version": "v1",
  "published": "2015-08-21T19:48:50.000Z",
  "updated": "2015-08-21T19:48:50.000Z",
  "title": "A Note On Immersion Intertwines Of Infinite Graphs",
  "authors": [
    "Matthew Barnes",
    "Bogdan Oporowski"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We present a construction of two infinite graphs $G_1$ and $G_2$, and of an infinite set $\\mathscr{F}$ of graphs such that $\\mathscr{F}$ is an antichain with respect to the immersion relation and, for each graph $G$ in $\\mathscr{F}$, both $G_1$ and $G_2$ are subgraphs of $G$, but no graph properly immersed in $G$ admits an immersion of $G_1$ and of $G_2$. This shows that the class of infinite graphs ordered by the immersion relation does not have the finite intertwine property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-21T19:48:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C63"
    ],
    "keywords": [
      "infinite graphs",
      "immersion intertwines",
      "immersion relation",
      "finite intertwine property",
      "infinite set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}