{
  "id": "1404.4064",
  "version": "v2",
  "published": "2014-04-15T20:11:18.000Z",
  "updated": "2014-10-28T22:06:50.000Z",
  "title": "Binomial partial Steiner triple systems containing complete graphs",
  "authors": [
    "M. Prażmowska",
    "K. Prażmowski"
  ],
  "comment": "Corresponding author: M. Pra\\.zmowska",
  "categories": [
    "math.CO"
  ],
  "abstract": "We propose a new approach to studies on partial Steiner triple systems consisting in determining complete graphs contained in them. We establish the structure which complete graphs yield in a minimal PSTS that contains them. As a by-product we introduce the notion of a binomial PSTS as a configuration with parameters of a minimal PSTS with a complete subgraph. A representation of binomial PSTS with at least a given number of its maximal complete subgraphs is given in terms of systems of perspectives. Finally, we prove that for each admissible integer there is a binomial PSTS with this number of maximal complete subgraphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-15T20:11:18.000Z",
      "title": "Binomial configurations which contain complete graphs: $K_n$-subgraphs of a $\\left(\\binom{n+1}{2}_{n-1} \\binom{n+1}{3}_3\\right)$-configuration",
      "abstract": "We propose to base a classification of partial Steiner triple systems on determining complete graphs contained (freely) in them. We establish the structure which complete graphs yield in a minimal PSTS that contains them. As a by-product we introduce the notion of a binomial PSTS as a configuration with parameters of a minimal PSTS with a complete subgraph. A representation of binomial PSTS with at least a given number of its maximal complete subgraphs is given in terms of systems of perspectives.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-28T22:06:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B30",
      "05C51",
      "05B40"
    ],
    "keywords": [
      "contain complete graphs",
      "binomial configurations",
      "partial steiner triple systems",
      "binomial psts",
      "minimal psts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.4064P"
    }
  }
}