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

Eon-Kyung Lee; Sang-Jin Lee

doi:10.4134/BKMS.b230291

Bulletin of the
Korean Mathematical Society BKMS

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

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Bull. Korean Math. Soc. 2024; 61(5): 1197-1209

Online first article March 21, 2024 Printed September 30, 2024

https://doi.org/10.4134/BKMS.b230291

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

Eon-Kyung Lee, Sang-Jin Lee

Sejong University; Konkuk University

Abstract

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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.

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

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

Supported by: The first author was partially supported by NRF-2018R1D1A1B07043291. The second author was partially supported by NRF-2018R1D1A1B07043268.