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

@inproceedings{Drmota2018MaximalIS, 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}}, booktitle={AofA}, year={2018} }

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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