Some remarks about factors of graphs

: A (g, f )-factor of a graph is a subset F of E such that for all v V, g(v) degF(v) f(v). Lovasz gave a necessary and sufficient condition for the existence of a (g, f )-factor. We extend, to the case of edge-weighted graphs, a result of Kano and Saito who showed that if g(v) < degE(v) < f(v) for any [0, 1], then a (g, f )-factor always exist. In addition, we use results of Anstee to provide new necessary and sufficient conditions for the existence of a (g, f )-factor.

• Type: Journal
• Year: 2008
• Where: JGT
• Authors: José R. Correa, Martín Matamala
• Keywords: Edge-weighted Graphs, JGT 2008, Lovasz, Sufficient Conditions