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The goal of this paper is to obtain quantitative results on the number and onthe size of maximal independent sets and maximal matchings in severalblock-stable graph classes that satisfy a proper sub-criticality condition. Inparticular we cover trees, cacti graphs and series-parallel graphs. The proofmethods are based on a generating function approach and a proper singularityanalysis of solutions of implicit systems of functional equations in severalvariables. As a byproduct, this method extends previous results of Meir andMoon for trees [Meir, Moon: On maximal independent sets of nodes in trees,Journal of Graph Theory 1988].

Maximal independent sets and maximal matchings in series-parallel and related graph classes