Corpus ID: 211205084

The (Generalized) Orthogonality Dimension of (Generalized) Kneser Graphs: Bounds and Applications

@article{Golovnev2020TheO,
  title={The (Generalized) Orthogonality Dimension of (Generalized) Kneser Graphs: Bounds and Applications},
  author={Alexander Golovnev and I. Haviv},
  journal={ArXiv},
  year={2020},
  volume={abs/2002.08580}
}
The orthogonality dimension of a graph $G=(V,E)$ over a field $\mathbb{F}$ is the smallest integer $t$ for which there exists an assignment of a vector $u_v \in \mathbb{F}^t$ with $\langle u_v,u_v \rangle \neq 0$ to every vertex $v \in V$, such that $\langle u_v, u_{v'} \rangle = 0$ whenever $v$ and $v'$ are adjacent vertices in $G$. The study of the orthogonality dimension of graphs is motivated by various application in information theory and in theoretical computer science. The contribution… Expand

References

SHOWING 1-10 OF 47 REFERENCES
Approximating the Orthogonality Dimension of Graphs and Hypergraphs
  • I. Haviv
  • Mathematics, Computer Science
  • MFCS
  • 2019
Approximating the independence number via theϑ-function
Matrix rigidity and the Croot-Lev-Pach lemma
Randomized graph products, chromatic numbers, and the Lovász ϑ-function
  • U. Feige
  • Mathematics, Computer Science
  • Comb.
  • 1997
On the orthogonal rank of Cayley graphs and impossibility of quantum round elimination
On Minrank and Forbidden Subgraphs
  • I. Haviv
  • Mathematics, Computer Science
  • APPROX-RANDOM
  • 2018
Improved hardness for H-colourings of G-colourable graphs
Topological Bounds on the Dimension of Orthogonal Representations of Graphs
  • I. Haviv
  • Mathematics, Computer Science
  • Eur. J. Comb.
  • 2019
Two Results Concerning Multicoloring
On the Quantum Chromatic Number of a Graph
...
1
2
3
4
5
...