The Grothendieck constant of a graph G = (V,E) is the least constant K such that for every matrix A : V × V → R: max f :V→S|V |−1 ∑ {u,v}∈E A(u, v) · 〈f(u), f(v)〉 ≤ K max :V→{−1,+1} ∑ {u,v}∈E A(u, v) · (u) (v). The investigation of this parameter, introduced in [2], is motivated by the algorithmic problem of maximizing the quadratic form ∑ {u,v}∈E A(u, v) (u) (v) over all : V → {−1, 1}, which a...