{
  "id": "1904.10244",
  "version": "v1",
  "published": "2019-04-23T11:02:12.000Z",
  "updated": "2019-04-23T11:02:12.000Z",
  "title": "Maximal independent sets and maximal matchings in series-parallel and related graph classes",
  "authors": [
    "Michael Drmota",
    "Lander Ramos",
    "Clément Requilé",
    "Juanjo Rué"
  ],
  "comment": "32 pages, 7 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The goal of this paper is to obtain quantitative results on the number and on the size of maximal independent sets and maximal matchings in several block-stable graph classes that satisfy a proper sub-criticality condition. In particular we cover trees, cacti graphs and series-parallel graphs. The proof methods are based on a generating function approach and a proper singularity analysis of solutions of implicit systems of functional equations in several variables. As a byproduct, this method extends previous results of Meir and Moon for trees [Meir, Moon: On maximal independent sets of nodes in trees, Journal of Graph Theory 1988].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-23T11:02:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximal independent sets",
      "related graph classes",
      "maximal matchings",
      "series-parallel",
      "proper sub-criticality condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}