The size of the approximate vertex cover is never more than twice the size of
the optimal vertex cover.
Approx-Vertex-Cover has a ratio bound of 2.
The approximate solution C is a vertex cover.
Let A be the set of edges chosen by the algorithm. Since each such edge's
endpoints were not in C at the time, C = 2A. An
optimal cover must have at least A vertices, C*A. Thus C* 1/2C and
2 = p.