Let G be a simple graph. Let g(x) and f(x) be integer-valued functions defined on V(G) with f(x) ≥ g(x) ≥ 1 for all x ∈ V(G). It is proved that if G is (mg+m–1,mf–m+1)-graph and H is a [1,2]-subgraph with m edges, then there exists a (g, f)-factorization of G orthogonal to H.
![(g, f)-factorizations of graphs orthogonal to [1,2]-subgraph](/resources/images/comingsoon.png)