{
  "id": "1702.07764",
  "version": "v1",
  "published": "2017-02-24T21:09:19.000Z",
  "updated": "2017-02-24T21:09:19.000Z",
  "title": "Coalescence and Minimal Spanning Trees of Irregular Graphs",
  "authors": [
    "Yevgeniy Kovchegov",
    "Peter T. Otto",
    "Anatoly Yambartsev"
  ],
  "comment": "35 pages",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "In this paper we devise a method of finding the limiting mean length of a minimal spanning tree for a random graph via the Smoluchowski coagulation equations for the corresponding coalescent process. In particular, we use this approach for finding the limiting mean length of a minimal spanning tree for the Erdos-Renyi random graph on an asymmetric bipartite graph, producing a completely new formula yet consistent with the previously known formula for the symmetric bipartite graph $K_{n,n}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-24T21:09:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "05C80"
    ],
    "keywords": [
      "minimal spanning tree",
      "irregular graphs",
      "limiting mean length",
      "coalescence",
      "asymmetric bipartite graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}