{
  "id": "1011.4888",
  "version": "v1",
  "published": "2010-11-22T17:55:20.000Z",
  "updated": "2010-11-22T17:55:20.000Z",
  "title": "On the heterochromatic number of hypergraphs associated to geometric graphs and to matroids",
  "authors": [
    "Juan José Montellano-Ballesteros",
    "Eduardo Rivera-Campo"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The heterochromatic number hc(H) of a non-empty hypergraph H is the smallest integer k such that for every colouring of the vertices of H with exactly k colours, there is a hyperedge of H all of whose vertices have different colours. We denote by nu(H) the number of vertices of H and by tau(H) the size of the smallest set containing at least two vertices of each hyperedge of H. For a complete geometric graph G with n > 2 vertices let H = H(G) be the hypergraph whose vertices are the edges of G and whose hyperedges are the edge sets of plane spanning trees of G. We prove that if G has at most one interior vertex, then hc(H) = nu(H) - tau(H) + 2. We also show that hc(H) = nu(H) - tau(H) + 2 whenever H is a hypergraph with vertex set and hyperedge set given by the ground set and the bases of a matroid, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-22T17:55:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hypergraphs",
      "heterochromatic number hc",
      "complete geometric graph",
      "non-empty hypergraph",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.4888J"
    }
  }
}