A discrete model for studying existence and uniqueness of solutions in nonlinear resistive circuits

Two combinatorial problems raised by the fundamental question of the existence and uniqueness of solutions in nonlinear electric circuits are presented. The first problem, namely the existence of a pair of conjugate trees, has been solved in polynomial time using an original model based on matroid intersection. For the second problem, which is the search of a particular orientation in a multigraph with labeled edges, an elaborate branch and bound procedure is proposed.