Cross-series-parallel digraphs

Series-parallel directed graphs have been generalized in various directions. Some of these generalizations control the structure of certain emerging induced subdigraphs called N's. They allow an efficient recognition by decomposition trees. We introduce another class of directed acyclic digraphs generalizing series-parallel directed graphs with less structure of induced N's. We show that they still can be efficiently recognized by a decomposition approach. In contrast, however, to the other mentioned generalization this decomposition is not unique and does not lead to a tree but a planar graph. (C) 2020 Elsevier B.V. All rights reserved