The Gram Dimension of a Graph

@inproceedings{Laurent2012TheGD,
  title={The Gram Dimension of a Graph},
  author={Monique Laurent and Antonios Varvitsiotis},
  booktitle={ISCO},
  year={2012}
}
The Gram dimension $\text{\rm gd}(G)$ of a graph is the smallest integer k≥1 such that, for every assignment of unit vectors to the nodes of the graph, there exists another assignment of unit vectors lying in ℝk, having the same inner products on the edges of the graph. The class of graphs satisfying $\text{\rm gd}(G) \le k$ is minor closed for fixed k, so it can characterized by a finite list of forbidden minors. For k≤3, the only forbidden minor is Kk+1. We show that a graph has Gram… 
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