Bulletin of the
Korean Mathematical Society

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Ahead of Print Articles


Bull. Korean Math. Soc.

Online first article March 21, 2024

Copyright © The Korean Mathematical Society.

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

Eon-Kyung Lee and Sang-Jin Lee

Sejong University, Konkuk University


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.

Keywords: right-angled Artin groups, extension graphs, translation length, biconnected graphs

MSC numbers: 20F36, 20F65, 20F69, 57M15, 57M60

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