Right-angled Artin groups on path graphs, cycle graphs and complete bipartite graphs

Abstract

For a finite simplicial graph $\Gamma$, let $G(\Gamma)$ denote the right-angled Artin group on the complement graph of $\Gamma$. For path graphs $P_k$, cycle graphs $C_\ell$ and complete bipartite graphs $K_{n, m}$, this article characterizes the embeddability of $G(K_{n, m})$ in $G(P_k)$ and in $G(C_\ell)$