{
  "id": "math/0408015",
  "version": "v3",
  "published": "2004-08-02T11:28:52.000Z",
  "updated": "2005-09-12T09:50:59.000Z",
  "title": "The homotopy type of complexes of graph homomorphisms between cycles",
  "authors": [
    "Sonja Lj. Cukic",
    "Dmitry N. Kozlov"
  ],
  "comment": "15 pages, 8 figures; Final version, to appear in Journal of Discrete and Computational Geometry",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we study the homotopy type of $\\Hom(C_m,C_n)$, where $C_k$ is the cyclic graph with $k$ vertices. We enumerate connected components of $\\Hom(C_m,C_n)$ and show that each such component is either homeomorphic to a point or homotopy equivalent to $S^1$. Moreover, we prove that $\\Hom(C_m,L_n)$ is either empty or is homotopy equivalent to the union of two points, where $L_n$ is an $n$-string, i.e., a tree with $n$ vertices and no branching points.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-09-12T09:50:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "57M15"
    ],
    "keywords": [
      "homotopy type",
      "graph homomorphisms",
      "homotopy equivalent",
      "cyclic graph",
      "enumerate connected components"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8015C"
    }
  }
}