Orthonormal representations, vector chromatic number, and extension complexity
Orthonormal representations, vector chromatic number, and extension complexity
Abstract We construct a bipartite generalization of Alon and Szegedy's nearly orthogonal vectors, thereby obtaining strong bounds for several extremal problems involving the Lovász theta function, vector chromatic number, minimum semidefinite rank, nonnegative rank, and extension complexity of polytopes. In particular, we answer a question from our previous work together …