Consider graphs over $n$ nodes. What is the maximum number of edges of a linklessly embeddable graph?
A more general question is the following. Given $\mu$ what is the maximum number of edges of graphs with the Colin de Verdiere number $\mu$?
A related question would be the following. Is there a fixed space (say a 2-manifold) such that a graph which embeds linklessly into $\mathbb{R}^3$ embeds in that space?
Thanks,