The Independence Number of the Orthogonality Graph in Dimension $2^k$

Ferdinand Ihringer; Hajime Tanaka

doi:10.1007/s00493-019-4134-9

The Independence Number of the Orthogonality Graph in Dimension $2^k$

Combinatorics 2021-11-02 v3

Authors: Ferdinand Ihringer , Hajime Tanaka

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Abstract

We determine the independence number of the orthogonality graph on $2^k$ -dimensional hypercubes. This answers a question by Galliard from 2001 which is motivated by a problem in quantum information theory. Our method is a modification of a rank argument due to Frankl who showed the analogous result for $4p^k$ -dimensional hypercubes, where $p$ is an odd prime.

Keywords

independence number orthogonality graph hypercube rank argument quantum information theory

Cite

@article{arxiv.1901.04860,
  title  = {The Independence Number of the Orthogonality Graph in Dimension $2^k$},
  author = {Ferdinand Ihringer and Hajime Tanaka},
  journal= {arXiv preprint arXiv:1901.04860},
  year   = {2021}
}

Comments

3 pages, accepted by Combinatorica, fixed a minor typo spotted by Peter Sin

The Independence Number of the Orthogonality Graph in Dimension $2^k$

Abstract

Keywords

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