(g, f)Factorizations Randomly Orthogonal to a Subgraph in Graphs

Let G be a graph with vertex set V (G) and edge set E(G) and let g and f be two integervalued functions defined on V (G) such that 2k 2 g(x) f(x) for all x V (G). Let H be a subgraph of G with mk edges. In this paper, it is proved that every (mg *m 1,mf m * 1)graph G has (g, f)factorizations randomly korthogonal to H under some special conditions.