An approximation of the minimum vertex cover in a graph

For a given undirected graphG withn vertices andm edges, we present an approximation algorithm for the minimum vertex cover problem. Our algorithm finds a vertex cover within\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$2 - \frac{{8m}}{{13n^2 + 8m}}$$ \end{document} of the optimal size inO(nm) time.