Orthonormal representations, vector chromatic number, and extension complexity
arXiv:2310.17482
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 derive a couple of general lower bounds for the vector chromatic number which may be of independent interest.
9 pages; Fixed minor typographical and logical errors