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We study various SDP formulations for {\\sc Vertex Cover} by adding different constraints to the standard formulation. We show that {\\sc Vertex Cover} cannot be approximated better than 2βo(1) even when we add the so called pentagonal inequality constraints to the standard SDP formulation, en route answering an open question of Karakostas~\\cite{Karakostas}. We further show the surprising fact that by strengthening the SDP with the (intractable) requirement that the metric interpretation of the solution is an ell1β metric, we get an exact relaxation (integrality gap is 1), and on the other hand if the solution is arbitrarily close to being ell1β embeddable, the integrality gap may be as big as 2βo(1). Finally, inspired by the above findings, we use ideas from the integrality gap construction of Charikar \\cite{Char02} to provide a family of simple examples for negative type metrics that cannot be embedded into ell1β with distortion better than 8/7βeps. To this end we prove a new isoperimetric inequality for the hypercube
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