• 대한수학회보
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• 제50권2호
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• pp.543-558
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• 2013

Let ${\Gamma}$ be a graph which contains two vertices $a$, $b$ with the same link. For the case where the link has less than 3 vertices, we prove that if the right-angled Artin group A(${\Gamma}$) contains a hyperbolic surface subgroup, then A(${\Gamma}$-{a}) contains a hyperbolic surface subgroup. Moreover, we also show that the same result holds with certain restrictions for the case where the link has more than or equal to 3 vertices.

• 대한수학회보
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• 제49권5호
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• pp.1057-1065
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• 2012

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.