{
  "id": "math/0307096",
  "version": "v3",
  "published": "2003-07-08T18:00:57.000Z",
  "updated": "2003-09-05T19:18:50.000Z",
  "title": "Rayleigh Matroids",
  "authors": [
    "Y. -B. Choe",
    "D. G. Wagner"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Motivated by a property of linear resistive electrical networks, we introduce the class of Rayleigh matroids. This is a subclass of the balanced matroids introduced by Feder and Mihail [FM] in 1992. We prove a variety of results relating Rayleigh matroids to other well-known classes -- in particular, we show that a binary matroid is Rayleigh if and only if it does not contain S_8 as a minor. This has the consequence that a binary matroid is balanced if and only if it is Rayleigh, and provides the first complete proof in print that S_8 is the only minor-minimal binary non-balanced matroid, as claimed in [FM]. We also give an example of a balanced matroid which is not Rayleigh.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-09-05T19:18:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "05A20",
      "05A15",
      "94C05"
    ],
    "keywords": [
      "binary matroid",
      "minor-minimal binary non-balanced matroid",
      "first complete proof",
      "results relating rayleigh matroids",
      "well-known classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......7096C"
    }
  }
}