{
  "id": "math/0408262",
  "version": "v2",
  "published": "2004-08-19T14:38:15.000Z",
  "updated": "2004-12-03T06:37:05.000Z",
  "title": "A simple proof for folds on both sides in complexes of graph homomorphisms",
  "authors": [
    "Dmitry N. Kozlov"
  ],
  "comment": "Final version, to appear in Proceedings of the American Mathematical Society",
  "journal": "Proc. Amer. Math. Soc. 134 (2006), no. 5, 1265--1270",
  "categories": [
    "math.CO",
    "math.AT"
  ],
  "abstract": "In this paper we study implications of folds in both parameters of Lov\\'asz' Hom(-,-) complexes. There is an important connection between the topological properties of these complexes and lower bounds for chromatic numbers. We give a very short and conceptual proof of the fact that if G-v is a fold of G, then Bd(Hom(G,H)) collapses onto Bd Hom(G-v,H), whereas Hom(H,G) collapses onto Hom(H,G-v). We also give an easy inductive proof of the only nonelementary fact which we use for our arguments: if $\\phi$ is a closure operator on P, then $\\Delta(P)$ collapses onto $\\Delta(\\phi(P))$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-12-03T06:37:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "57M15"
    ],
    "keywords": [
      "simple proof",
      "graph homomorphisms",
      "lower bounds",
      "closure operator",
      "nonelementary fact"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8262K"
    }
  }
}