The $R_{\mathrm{\infty }}$-property for right-angled Artin groups and their nilpotent quotients

It is proven that every non-abelian right-angled Artin group has the $R_{\mathrm{\infty }}$-property and bounds are given on the $R_{\mathrm{\infty }}$-nilpotency index. In case the graph is transposition-free, which is true for almost all graphs, it is shown that the $R_{\mathrm{\infty }}$-nilpotency index is equal to 2.