Orthogonal (g, f)-factorizations of bipartite graph

Abstract

We consider 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). A (g, f) - factor of a graph G is a spanning subgraph F of G such that g(x) ≤ dF(x) ≤ f(x) for each vertex x of F. In this paper, we mainly discuss the problem of orthogonal (g, f) -factorizations of bipartite graph. Furthermore, we generalized some predecessor’s result. © 1998 by the University of Notre Dame. All rights reserved.