Subgroup Separability of Artin Groups II

In this paper, we establish a new criterion for determining whether an Artin group is subgroup separable (LERF), building upon a criterion introduced in a previous work. Specifically, we prove an Artin group is LERF if and only if it does not contain certain induced subgraphs, thus providing a more direct generalization of the Metaftsis-Raptis criterion for RAAGs. As consequences, we prove an Artin group is ERF if and only if it is a free abelian group and we establish a link between subgroup separability and coherence for Artin groups.