Maximum (g,f)-factors of a general graph

AbstractThis paper presents a characterization of maximum (g,f)-factors of a general graph in which multiple edges and loops are allowed. An analogous characterization of the minimum (g,f)-factors of a general graph is also presented. In addition, we obtain a transformation theorem for any two general graphs on the same vertex set. As special cases, we have the transformation theorems for both maximum (g,f)-factors and minimum (g,f)-factors. Our results generalize some of C. Berge's results on maximum matchings and maximum c-matchings of a multiple graph