Orthonormal representations, vector chromatic number, and extension complexity
Combinatorics
2023-11-07 v2 Discrete Mathematics
Abstract
We construct a bipartite generalization of Alon and Szegedy's nearly orthogonal vectors, thereby obtaining strong bounds for several extremal problems involving the Lov\'asz 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.
Cite
@article{arxiv.2310.17482,
title = {Orthonormal representations, vector chromatic number, and extension complexity},
author = {Igor Balla},
journal= {arXiv preprint arXiv:2310.17482},
year = {2023}
}
Comments
9 pages; Fixed minor typographical and logical errors