{
  "id": "1512.02911",
  "version": "v1",
  "published": "2015-12-09T15:52:27.000Z",
  "updated": "2015-12-09T15:52:27.000Z",
  "title": "The colouring number of infinite graphs",
  "authors": [
    "Nathan Bowler",
    "Johannes Carmesin",
    "Christian Reiher"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that, given an infinite cardinal $\\mu$, a graph has colouring number at most $\\mu$ if and only if it contains neither of two types of subgraph. We also show that every graph with infinite colouring number has a well-ordering of its vertices that simultaneously witnesses its colouring number and its cardinality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-09T15:52:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C63",
      "05C15",
      "03E05"
    ],
    "keywords": [
      "infinite graphs",
      "infinite cardinal",
      "infinite colouring number",
      "cardinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151202911B"
    }
  }
}