  In this paper we study irreducibility in RNA structures. By RNA structure we
mean RNA secondary as well as RNA pseudoknot structures. In our analysis we
shall contrast random and minimum free energy (mfe) configurations. We compute
various distributions: of the numbers of irreducible substructures, their
locations and sizes, parameterized in terms of the maximal number of mutually
crossing arcs, $k-1$, and the minimal size of stacks $\sigma$. In particular,
we analyze the size of the largest irreducible substructure for random and mfe
structures, which is the key factor for the folding time of mfe configurations.
