{
  "id": "0811.3500",
  "version": "v1",
  "published": "2008-11-21T15:18:33.000Z",
  "updated": "2008-11-21T15:18:33.000Z",
  "title": "Pivots, Determinants, and Perfect Matchings of Graphs",
  "authors": [
    "Robert Brijder",
    "Tero Harju",
    "Hendrik Jan Hoogeboom"
  ],
  "comment": "16 pages",
  "journal": "Theoretical Computer Science 454 (2012) 64-71",
  "doi": "10.1016/j.tcs.2012.02.031",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a characterization of the effect of sequences of pivot operations on a graph by relating it to determinants of adjacency matrices. This allows us to deduce that two sequences of pivot operations are equivalent iff they contain the same set S of vertices (modulo two). Moreover, given a set of vertices S, we characterize whether or not such a sequence using precisely the vertices of S exists. We also relate pivots to perfect matchings to obtain a graph-theoretical characterization. Finally, we consider graphs with self-loops to carry over the results to sequences containing both pivots and local complementation operations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-21T15:18:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perfect matchings",
      "determinants",
      "pivot operations",
      "local complementation operations",
      "adjacency matrices"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.3500B"
    }
  }
}