{
  "id": "2301.08707",
  "version": "v1",
  "published": "2023-01-20T18:04:53.000Z",
  "updated": "2023-01-20T18:04:53.000Z",
  "title": "Separating the edges of a graph by a linear number of paths",
  "authors": [
    "Marthe Bonamy",
    "Fábio Botler",
    "François Dross",
    "Tássio Naia",
    "Jozef Skokan"
  ],
  "comment": "6 pages, 2 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "Recently, Letzter proved that any graph of order $n$ contains a collection $\\mathcal{P}$ of $O(n\\log^\\star n)$ paths with the following property: for all distinct edges $e$ and $f$ there exists a path in $\\mathcal{P}$ which contains $e$ but not $f$. We improve this upper bound to $19 n$, thus answering a question of Katona and confirming a conjecture independently posed by Balogh, Csaba, Martin, and Pluh\\'ar and by Falgas-Ravry, Kittipassorn, Kor\\'andi, Letzter, and Narayanan. Our proof is elementary and self-contained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-20T18:04:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear number",
      "upper bound",
      "separating",
      "distinct edges",
      "collection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}