Hoffmann, A. & Volkmann, L. Graphs and Combinatorics (2005) 21: 421. doi:10.1007/s00373-005-0631-2
In this note we will derive some structural results for a bipartite graph G with a unique f-factor. Two necessary conditions will be that G is saturated, meaning that the addition of any edge leads to a second f-factor, and that fA, fB≥1. Here fA and fB are defined as the minimum of f over the vertices in the two partite sets A and B of G, respectively. Our main result states that G has at least fA + fB vertices for which dG (v) = f(v) holds.