Maximal Independent Sets and Maximal Matchings in Series-Parallel and Related Graph Classes

  title={Maximal Independent Sets and Maximal Matchings in Series-Parallel and Related Graph Classes},
  author={M. Drmota and L. Ramos and Cl{\'e}ment Requil{\'e} and J. Ru{\'e}},
  • M. Drmota, L. Ramos, +1 author J. Rué
  • Published in AofA 2018
  • Computer Science, Mathematics
  • 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. 

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