Co-contractions of graphs and right-angled Coxeter groups
Bull. Korean Math. Soc. 2012 Vol. 49, No. 5, 1057-1065
https://doi.org/10.4134/BKMS.2012.49.5.1057
Printed September 30, 2012
Jongtae Kim and Myoungho Moon
Konkuk University, Konkuk University
Abstract : 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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