A note on higher coherence of graphs of groups

For n ∈ N n , a group is called 𝑛-coherent if every subgroup of type F n Fₙ is of type F n + 1 Fₙ₊₁ . For n ≥ 1 n≥ 1 , we observe that graphs of groups with 𝑛-coherent vertex groups and virtually poly-cyclic edge groups are 𝑛-coherent. We deduce the 𝑛-coherence of certain right-angled Artin groups.