{
  "id": "1309.0416",
  "version": "v1",
  "published": "2013-09-02T14:18:45.000Z",
  "updated": "2013-09-02T14:18:45.000Z",
  "title": "Distinguishing homomorphisms of infinite graphs",
  "authors": [
    "Anthony Bonato",
    "Dejan Delic"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper $n$-colourings are generalized to the new notion of distinguishing homomorphisms. We prove that if a graph $G$ satisfies the connected existentially closed property and admits a homomorphism to $H$, then it admits continuum-many distinguishing homomorphisms from $G$ to $H$ join $K_2.$ Applications are given to a family universal $H$-colourable graphs, for $H$ a finite core.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-02T14:18:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinite graphs",
      "admits continuum-many distinguishing homomorphisms",
      "adjacency property",
      "distinguishing chromatic number",
      "upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.0416B"
    }
  }
}