Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Drmota, Michael; Ramos, Lander; Requilé, Clément; Rué, Juanjo http://www.dagstuhl.de/lipics License
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Maximal Independent Sets and Maximal Matchings in Series-Parallel and Related Graph Classes

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Abstract

We provide combinatorial decompositions as well as asymptotic tight estimates for two maximal parameters: the number and average size of maximal independent sets and maximal matchings in series-parallel graphs (and related graph classes) with n vertices. In particular, our results extend previous results of Meir and Moon for trees [Meir, Moon: On maximal independent sets of nodes in trees, Journal of Graph Theory 1988]. We also show that these two parameters converge to a central limit law.

BibTeX - Entry

@InProceedings{drmota_et_al:LIPIcs:2018:8911,
  author =	{Michael Drmota and Lander Ramos and Cl{\'e}ment Requil{\'e} and Juanjo Ru{\'e}},
  title =	{{Maximal Independent Sets and Maximal Matchings in Series-Parallel and Related Graph Classes}},
  booktitle =	{29th International Conference on Probabilistic,  Combinatorial and Asymptotic Methods for the Analysis of Algorithms  (AofA 2018)},
  pages =	{18:1--18:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{James Allen Fill and Mark Daniel Ward},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8911},
  URN =		{urn:nbn:de:0030-drops-89117},
  doi =		{10.4230/LIPIcs.AofA.2018.18},
  annote =	{Keywords: Asymptotic enumeration, central limit laws, subcritical graph classes, maximal independent set, maximal matching}
}

Keywords: Asymptotic enumeration, central limit laws, subcritical graph classes, maximal independent set, maximal matching
Seminar: 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)
Issue date: 2018
Date of publication: 2018


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