{
  "id": "2212.10354",
  "version": "v1",
  "published": "2022-12-17T17:16:08.000Z",
  "updated": "2022-12-17T17:16:08.000Z",
  "title": "Edge Contraction and Line Graphs",
  "authors": [
    "Hany Ibrahim",
    "Peter Tittmann"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2203.03491",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a family of graphs $\\mathcal{H}$, a graph $G$ is $\\mathcal{H}$-free if any subset of $V(G)$ does not induce a subgraph of $G$ that is isomorphic to any graph in $\\mathcal{H}$. We present sufficient and necessary conditions for a graph $G$ such that $G/e$ is $\\mathcal{H}$-free for any edge $e$ in $E(G)$. Thereafter, we use these conditions to characterize claw-free, matrogenic and line graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-17T17:16:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "line graphs",
      "edge contraction",
      "necessary conditions",
      "matrogenic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}