Tselekidis's asymptotic-dimension bound for Coxeter groups

Let $\Gamma$ be a finite simplicial labeled graph, and let $A_\Gamma$ and $W_\Gamma$ denote the Artin and Coxeter groups associated to $\Gamma$. Define

$$Sim(\Gamma)=\max\{n\mid \Gamma\text{ contains the 1-skeleton of the standard }(n-1)\text{-simplex }\Delta^{n-1}\}.$$

Tselekidis's conjecture. The asymptotic dimension of the Coxeter group satisfies

$$\operatorname{asdim} W_\Gamma\leq Sim(\Gamma)$$

for all Coxeter groups.

This conjecture is presented alongside the analogous Artin-group bound as part of the paper's program on asymptotic dimension. The supplied text gives no resolution or partial result for this Coxeter-group inequality, so its general validity remains open.