$K(\pi,1)$-conjecture ofr Artin groups behave well with respect to special subgroups. Reference-Request

Question

For a proof for an article I would need the following result:

If $A_\Gamma$ is an Artin group such that the $K(\pi,1)$-conjecture holds for it and $\Gamma'\subset\Gamma$ is an induced subgraph, then the $K(\pi,1)$-conjecture holds for $A_{\Gamma'}$.

I've searched in all the references I know about this conjecture, but none of them seems to prove this fact. My question is if you know whether this has been proved or not, and in case it its where I can find it.

Thanks in advance.

Answer 1

Yes, it has been proved by Godelle and Paris, it is cited as Theorem 5.5 in the article https://arxiv.org/pdf/1211.7339 by Paris (and Theorem 3.1 for the equivalence with the K(pi,1) conjecture).