{
  "id": "2408.04802",
  "version": "v1",
  "published": "2024-08-09T01:06:21.000Z",
  "updated": "2024-08-09T01:06:21.000Z",
  "title": "Homotopy types of Hom complexes of graph homomorphisms whose codomains are cycles",
  "authors": [
    "Soichiro Fujii",
    "Yuni Iwamasa",
    "Kei Kimura",
    "Yuta Nozaki",
    "Akira Suzuki"
  ],
  "comment": "11 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "For simple graphs $G$ and $H$, the Hom complex $\\mathrm{Hom}(G,H)$ is a polyhedral complex whose vertices are the graph homomorphisms $G\\to H$. It is known that $\\mathrm{Hom}(G,H)$ is homotopy equivalent to a disjoint union of points and circles when both $G$ and $H$ are cycles. We generalize this known result by showing that $\\mathrm{Hom}(G,H)$ is homotopy equivalent to a disjoint union of points and circles whenever $G$ is connected and $H$ is a cycle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-09T01:06:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55U05",
      "05C15",
      "55P15"
    ],
    "keywords": [
      "graph homomorphisms",
      "hom complex",
      "homotopy types",
      "homotopy equivalent",
      "disjoint union"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}