Characterization of Bestvina–Brady groups that are right-angled Artin groups

Characterize the finite simplicial graphs whose Bestvina–Brady groups are right-angled Artin groups, resolving the general case beyond the classes established in the paper.

Background

For a finite simplicial graph Γ, the Bestvina–Brady group B_Γ is defined as the kernel of the length character from the associated right-angled Artin group G_Γ to the integers. The paper studies when subgroups of B_Γ are right-angled Artin groups and gives a complete characterization for the stronger property that every subgroup of B_Γ is a right-angled Artin group.

The authors explicitly note that the more basic problem of determining when B_Γ itself is a right-angled Artin group is unresolved in general. This remains distinct from the paper’s classification theorem for graphs whose Bestvina–Brady groups have all subgroups right-angled Artin.