2 problems

Let $G$ be a group, let $S$ be a connection set, and let $\operatorname{Cay}(G,S)$ be the corresponding Cayley graph. Consider induced subgraphs whose vertex sets contain more than…

Let $G$ be the Cayley graph of a Coxeter group, and let $Q_d$ be the largest subgraph of $G$ isomorphic to a cube. Write $\boldsymbol{\kappa}(G)=d$ for its dimension, and let…