A DISCRETE MODEL FOR STUDYING EXISTENCE AND UNIQUENESS OF SOLUTIONS IN NONLINEAR RESISTIVE CIRCUITS

Two combinatorial problems raised by the fundamental question of the e xistence and uniqueness of solutions in nonlinear electric circuits ar e presented. The first problem, namely the existence of a pair of conj ugate trees, has been solved in polynomial time using an original mode l 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.