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In this paper we construct an approximation algorithm for the Minimum VertexCover Problem (Min-VC) with an expected approximation ratio of 2-f(beta) forrandom Power Law Graphs (PLG) in the (alpha,beta)-model of Aiello et. al.,where f(beta) is a strictly positive function of the parameter beta. We obtainthis result by combining the Nemhauser and Trotter approach for Min-VC with anew deterministic rounding procedure which achieves an approximation ratio of3/2 on a subset of low degree vertices for which the expected contribution tothe cost of the associated linear program is sufficiently large.

Approximability of the Vertex Cover Problem in Power Law Graphs