Stability Number and f-Factors in Graphs

Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f:V \longrightarrow N}$$\end{document} be an integer function. An f-factor is a spanning subgraph of a graph G = (V,E) whose vertices have degrees defined by f. In this paper, we prove sufficient condition for the existence of a f-factor which involves the stability number, the minimum degree of G or the connectivity of the graph.