Path Factorization Induced Network Flow

In path factorization Ushio [8] gave the necessary and sufficient conditions for design. When is an even number, the spectrum problem is completely solved [9, 1]. For odd value of the problem was studied by several researchers [7, 10, 11, 5, 2, 6]. In all these papers [7, 10, 11, 5, 2, 6] Ushio Conjecture [8] played an important role. Here in this paper we obtain a feasible network flow consisting of path factors of a bipartite graph satisfying the conditions of path factorization. Mathematics Subject Classification 2010: 68R10, 05C21, 05C70.