{
  "id": "1407.3604",
  "version": "v1",
  "published": "2014-07-14T11:03:23.000Z",
  "updated": "2014-07-14T11:03:23.000Z",
  "title": "Davies-trees in infinite combinatorics",
  "authors": [
    "Daniel T. Soukup"
  ],
  "comment": "8 pages, prepared for the Logic Colloquium 2014",
  "categories": [
    "math.LO",
    "math.CO"
  ],
  "abstract": "This short note, prepared for the Logic Colloquium 2014, provides an introduction to Davies-trees and presents new applications in infinite combinatorics. In particular, we give new and simple proofs to the following theorems of P. Komj\\'ath: every $n$-almost disjoint family of sets is essentially disjoint for any $n\\in \\mathbb N$; $\\mathbb R^2$ is the union of $n+2$ clouds if the continuum is at most $\\aleph_n$ for any $n\\in \\mathbb N$; every uncountably chromatic graph contains $n$-connected uncountably chromatic subgraphs for every $n\\in \\mathbb N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-14T11:03:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05",
      "03C98",
      "05C63"
    ],
    "keywords": [
      "infinite combinatorics",
      "davies-trees",
      "uncountably chromatic graph contains",
      "short note",
      "logic colloquium"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.3604S"
    }
  }
}