{
  "id": "2403.09518",
  "version": "v1",
  "published": "2024-03-14T16:02:01.000Z",
  "updated": "2024-03-14T16:02:01.000Z",
  "title": "About Berge-Füredi's conjecture on the chromatic index of hypergraphs",
  "authors": [
    "Alain Bretto",
    "Alain Faisant",
    "François Hennecart"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that the chromatic index of a hypergraph $\\mathcal{H}$ satisfies Berge-F\\\"uredi conjectured bound $\\mathrm{q}(\\mathcal{H})\\le \\Delta([\\mathcal{H}]_2)+1$ under certain hypotheses on the antirank $\\mathrm{ar}(\\mathcal{H})$ or on the maximum degree $\\Delta(\\mathcal{H})$. This provides sharp information in connection with Erd\\H{o}s-Faber-Lov\\'asz Conjecture which deals with the coloring of a family of cliques that intersect pairwise in at most one vertex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-14T16:02:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "chromatic index",
      "berge-füredis conjecture",
      "hypergraph",
      "maximum degree",
      "sharp information"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}