{
  "id": "1805.00535",
  "version": "v1",
  "published": "2018-05-01T20:05:41.000Z",
  "updated": "2018-05-01T20:05:41.000Z",
  "title": "Hamiltonicity of $2$-block intersection graphs of ${\\rm{TS}}(v,λ)$: $v\\equiv 0$ or $4\\pmod{12}$",
  "authors": [
    "John Asplund",
    "Melissa Keranen"
  ],
  "comment": "19 pages, 23 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A ${\\rm{TS}}(v,\\lambda)$ is a pair $(V,\\mathcal{B})$ where $V$ contains $v$ points and $\\mathcal{B}$ contains $3$-element subsets of $V$ so that each pair in $V$ appears in exactly $\\lambda$ blocks. A $2$-block intersection graph ($2$-BIG) of a ${\\rm{TS}}(v,\\lambda)$ is a graph where each vertex is represented by a block from the ${\\rm{TS}}(v,\\lambda)$ and each pair of blocks $B_i,B_j\\in \\mathcal{B}$ are joined by an edge if $|B_i\\cap B_j|=2$. Using constructions for ${\\rm{TS}}(v,\\lambda)$ given by Schreiber, we show that there exists a ${\\rm{TS}}(v,\\lambda)$ for $v\\equiv 0$ or $4\\pmod{12}$ whose $2$-BIG is Hamiltonian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-01T20:05:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C45",
      "05C51"
    ],
    "keywords": [
      "block intersection graph",
      "hamiltonicity",
      "element subsets",
      "hamiltonian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}