Digraph decompositions and Eulerian systems

The theory of digraph decompositions introduced by W. Cunningham and the theory of isotropic systems introduced by the author are unified. A basic combinatorial tool is the operation of local complementation at a vertex of a digraph, a generalization of the similar operation already known for simple graphs. This allows us to unify in a single class the semibrittle digraphs characterized by W. Cunningham and to devise a more efficient algorithm for searching for a split of a digraph.