Integrality Gap of the Vertex Cover Linear Programming Relaxation

Abstract

We give a characterization result for the integrality gap of the natural linear programming relaxation for the vertex cover problem. We show that integrality gap of the standard linear programming relaxation for any graph G equals $\left(2-\frac{2}{{\chi }^f(G)}\right)$ where ${\chi }^f(G)$ denotes the fractional chromatic number of G.

6 pages