{
  "id": "1607.07426",
  "version": "v1",
  "published": "2016-07-25T19:45:45.000Z",
  "updated": "2016-07-25T19:45:45.000Z",
  "title": "Symmetric Graphs have symmetric Matchings",
  "authors": [
    "Jan Fricke"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Assume that there is a free group action of automorphisms on a bipartite graph. If there is a perfect matching on the factor graph, then obviously there is a perfect matching on the graph. Surprisingly, the reversed is also true for amenable groups: if there is a perfect matching on the graph, there is also a perfect matching on the factor graph, i. e. a group invariant (\"symmetric\") perfect matching on the graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-25T19:45:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric graphs",
      "symmetric matchings",
      "perfect matching",
      "factor graph",
      "free group action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}