Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2012; 49(5): 1057-1065

Printed September 30, 2012

https://doi.org/10.4134/BKMS.2012.49.5.1057

Copyright © The Korean Mathematical Society.

Co-contractions of graphs and right-angled Coxeter groups

Jongtae Kim and Myoungho Moon

Konkuk University, Konkuk University

Abstract

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We prove that if $\widehat{\Gamma}$ is a co-contraction of $\Gamma$, then the right-angled Coxeter group $C(\widehat{\Gamma})$ embeds into $C(\Gamma)$. Further, we provide a graph $\Gamma$ without an induced long cycle while $C(\Gamma)$ does not contain a hyperbolic surface group.

Keywords: right-angled Artin group, right-angled Coxeter group, hyperbolic surface subgroup

MSC numbers: Primary 20F36, 20F55, 20F65; Secondary 05C25

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