On conjugacy separability of graph products of groups

We show that the class of CC-hereditarily conjugacy separable groups is closed under taking arbitrary graph products whenever the class CC is an extension closed variety of finite groups. As a consequence we show that the class of CC-conjugacy separable groups is closed under taking arbitrary graph products. In particular, we show that right angled Coxeter groups are hereditarily conjugacy separable and 2-hereditarily conjugacy separable, and we show that infinitely generated right angled Artin groups are hereditarily conjugacy separable and p-hereditarily conjugacy separable for every prime number p.