Randomly Orthogonal (g,f)-factorizations in Graphs

Abstract

Let G be a graph with vertex set V (G )a nd edge setE(G )a nd letg and f be two integer-valued functions defined on V (G) such that 2k − 1 ≤ 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 and shown that the result is best possible.