{
  "id": "1409.2922",
  "version": "v1",
  "published": "2014-09-09T23:50:55.000Z",
  "updated": "2014-09-09T23:50:55.000Z",
  "title": "Trees, ladders and graphs",
  "authors": [
    "Dániel T. Soukup"
  ],
  "comment": "23 pages, 2 figures, submitted to the Journal of Comb. Theory Series B",
  "categories": [
    "math.CO",
    "math.LO"
  ],
  "abstract": "We introduce a new method to construct uncountably chromatic graphs from non special trees and ladder systems. Answering a question of P. Erd\\H{o}s and A. Hajnal from 1985, we construct graphs of chromatic number $\\omega_1$ without uncountable $\\omega$-connected subgraphs. Second, we build triangle free graphs of chromatic number $\\omega_1$ without subgraphs isomorphic to $H_{\\omega,\\omega+2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-09T23:50:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C63",
      "05C15",
      "03E05"
    ],
    "keywords": [
      "chromatic number",
      "build triangle free graphs",
      "construct uncountably chromatic graphs",
      "non special trees",
      "ladder systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.2922S"
    }
  }
}