The Colin de Verdière parameter and algebraic shifting

Let $G$ be a graph, let $\mu(G)$ denote the Colin de Verdière parameter of $G$, and let $k$ be a positive integer. Let $\Delta(G)$ denote either the symmetric or exterior algebraic shifting of $G$. Colin de Verdière shifting conjecture. If $\mu(G)\leq k$, then

$$\{k+1,k+2\}\notin \Delta(G).$$

This would relate the Colin de Verdière parameter to the shifted graph and, via the shifted-graph characterization of colorability, imply a corresponding bound on its chromatic number. The supplied text does not state whether the conjecture has been resolved.