{
  "id": "math/9809092",
  "version": "v1",
  "published": "1998-09-17T09:35:05.000Z",
  "updated": "1998-09-17T09:35:05.000Z",
  "title": "Graphs, flags and partitions",
  "authors": [
    "Jonathan Fine"
  ],
  "comment": "12 pages, LaTeX 2e, no figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper defines, for each graph $G$, a flag vector $fG$. The flag vectors of the graphs on $n$ vertices span a space whose dimension is $p(n)$, the number of partitions on $n$. The analogy with convex polytopes indicates that the linear inequalities satisfied by $fG$ may be both interesting and accessible. Such would provide inequalities both sharp and subtle on the combinatorial structure of $G$. These may be related to Ramsey theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-09-17T09:35:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B05"
    ],
    "keywords": [
      "partitions",
      "flag vector",
      "ramsey theory",
      "paper defines",
      "convex polytopes"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......9092F"
    }
  }
}