An upper bound of the minimal asymptotic translation length of right-angled Artin groups on extension graphs

Abstract

For the right-angled Artin group action on the extension graph, it is known that the minimal asymptotic translation length is bounded above by 2 provided that the defining graph has diameter at least 3. In this paper, we show that the same result holds without any assumption. This is done by exploring some graph theoretic properties of biconnected graphs, i.e. connected graphs whose complement is also connected.