Splittings of right-angled Artin groups

Abstract

We show that if a right-angled Artin group $A(\hat{I}“)$ has a non-trivial, minimal action on a tree $T$ which is not a line, then $\hat{I}“$ contains a separating subgraph $\hat{I}›$ such that $A(\hat{I}›)$ stabilizes an edge in $T$.