{
  "id": "1809.10100",
  "version": "v1",
  "published": "2018-09-26T16:16:32.000Z",
  "updated": "2018-09-26T16:16:32.000Z",
  "title": "Electrical networks and frame matroids",
  "authors": [
    "Bob Lutz"
  ],
  "comment": "22 pages, 9 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper defines Dirichlet matroids, a class of matroids arising from electrical networks and almost-balanced biased graphs. We prove four main results. First we use properties of the electrical response matrix to show that every Dirichlet matroid has the half-plane property. Second we bound the coefficients of the precoloring polynomial in terms of the chromatic polynomial. Third we prove a simple characterization of 3-connected Dirichlet matroids. And fourth we prove a circular network analog of the duality theorem for planar graphic matroids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-26T16:16:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "05C22",
      "05C15",
      "05C40",
      "34B45"
    ],
    "keywords": [
      "electrical networks",
      "frame matroids",
      "paper defines dirichlet matroids",
      "circular network analog",
      "planar graphic matroids"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}