Some remarks about factors of graphs
José Correa, Martı́n Matamala · Journal of Graph Theory · 2008
Abstract A ( g , f )‐factor of a graph is a subset F of E such that for all $v \in V$ , $g(v)\le {\rm deg}_{F}(v)\le f(v)$ . 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 $g(v)< \lambda {\rm deg}_{E}(v) < f (v)$ for any $\lambda\in [0,1]$ , 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. © 2008 Wiley Periodicals, Inc. J Graph Theory 57: 265–274, 2008