Partitioning RNAs into pseudonotted and pseudoknot-free regions modeled   as Dual Graphs
  Dual graphs have been applied to model RNA secondary structures. The purpose of the paper is two-fold: we present new graph-theoretic properties of dual graphs to validate the further analysis and classification of RNAs using these topological representations; we also present a linear-time algorithm to partition dual graphs into topological components called {\it blocks} and determine if each block contains a {\it pseudoknot} or not. We show that a block contains a pseudoknot if and only if the block has a vertex of degree $3$ or more; this characterization allows us to efficiently isolate smaller RNA fragments and classify them as pseudoknotted or pseudoknot-free regions, while keeping these sub-structures intact. Even though non-topological techniques to detect and classify pseudoknots have been efficiently applied, structural properties of dual graphs provide a unique perspective for the further analysis of RNAs. Applications to RNA design can be envisioned since modular building blocks with intact pseudoknots can be combined to form new constructs.\end{abstract} 
Louis Petingi and Tamar Schlick
q-bio.QM q-bio.BM