{
  "id": "1301.7356",
  "version": "v1",
  "published": "2013-01-30T20:58:17.000Z",
  "updated": "2013-01-30T20:58:17.000Z",
  "title": "Fractional Perfect b-Matching Polytopes. I: General Theory",
  "authors": [
    "Roger E. Behrend"
  ],
  "comment": "37 pages",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "The fractional perfect b-matching polytope of an undirected graph G is the polytope of all assignments of nonnegative real numbers to the edges of G such that the sum of the numbers over all edges incident to any vertex v is a prescribed nonnegative number b_v. General theorems which provide conditions for nonemptiness, give a formula for the dimension, and characterize the vertices, edges and face lattices of such polytopes are obtained. Many of these results are expressed in terms of certain spanning subgraphs of G which are associated with subsets or elements of the polytope. For example, it is shown that an element u of the fractional perfect b-matching polytope of G is a vertex of the polytope if and only if each component of the graph of u either is acyclic or else contains exactly one cycle with that cycle having odd length, where the graph of u is defined to be the spanning subgraph of G whose edges are those at which u is positive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-30T20:58:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B05",
      "05C50",
      "05C70",
      "52B11",
      "90C27",
      "90C35"
    ],
    "keywords": [
      "fractional perfect b-matching polytope",
      "general theory",
      "spanning subgraph",
      "nonnegative real numbers",
      "face lattices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.7356B"
    }
  }
}