On F-Hamiltonian for Bipartite Graph

Let G be a simple graph for each edge e=uv of graph G , let d(e)=d(u)+d(v),where d(u) and d(v) are degree of the vertices u and v respectively. Surpose G=(A,B;E) is bipartite graph, F is a 1-factor of G , G is called F-Hamiltonian if there exsiste a Hamilton cycle containing F in G.A necessary and sufficient condition is given for bipartite graph G=(A,B,E) to be F-Hamiltonian.