{
  "id": "2004.02162",
  "version": "v1",
  "published": "2020-04-05T11:24:46.000Z",
  "updated": "2020-04-05T11:24:46.000Z",
  "title": "Dilworth's Theorem for Borel Posets",
  "authors": [
    "Bartłomiej Bosek",
    "Jarosław Grytczuk",
    "Zbigniew Lonc"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A famous theorem of Dilworth asserts that any finite poset of width $k$ can be decomposed into $k$ chains. We study the following problem: given a Borel poset $P$ of finite width $k$, is it true that it can be decomposed into $k$ Borel chains? We give a positive answer in a special case of Borel posets embeddable into the real line. We also prove a dual theorem for posets whose comparability graphs are locally countable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-05T11:24:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dilworths theorem",
      "comparability graphs",
      "dilworth asserts",
      "finite width",
      "finite poset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}