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arXiv · 1802.03920

On Minrank and the Lov\'asz Theta Function

Ishay Haviv
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Abstract

Two classical upper bounds on the Shannon capacity of graphs are the $\vartheta$-function due to Lov\'asz and the minrank parameter due to Haemers. We provide several explicit constructions of $n$-vertex graphs with a constant $\vartheta$-function and minrank at least $n^\delta$ for a constant $\delta>0$ (over various prime order fields). This implies a limitation on the $\vartheta$-function-based algorithmic approach to approximating the minrank parameter of graphs. The proofs involve linear spaces of multivariate polynomials and the method of higher incidence matrices.

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Ishay Haviv. 2018-02-12. On Minrank and the Lov\'asz Theta Function. https://arxiv.org/abs/1802.03920

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