{
  "id": "1807.10498",
  "version": "v1",
  "published": "2018-07-27T09:00:33.000Z",
  "updated": "2018-07-27T09:00:33.000Z",
  "title": "Hom complexes of graphs of diameter $1$",
  "authors": [
    "Anurag Singh",
    "Nandini Nilakantan"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a finite, simplicial complex $X$ and a connected graph $T$ with diameter $1$, in this article, we show that $\\text{Hom}(T, G_{1, X})$ is homotopy equivalent to $X.$ Here, $G_{1,X}$ is the reflexive graph obtained by taking the $1$-skeleton of the first barycentric subdivision of $X$ and adding a loop at each vertex. This problem was proposed by Dochtermann in \\cite{anton}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-27T09:00:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "57M15"
    ],
    "keywords": [
      "hom complexes",
      "first barycentric subdivision",
      "simplicial complex",
      "homotopy equivalent",
      "dochtermann"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}