(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 k–orthogonal to H under some special conditions.