3 problems

Let $H$ be a planar graph. A $K$-fat minor-model of $H$ is a $K$-fat model of $H$, and $B_G(Z,cK)$ denotes the ball of radius $cK$ around $Z$ in $G$. Then there exists a constant…

Let $K,d,n\in\mathbb{N}$. A graph has a $K$-fat $(n\times n)$-grid minor when it contains the corresponding fat minor model. Then there exists some $g\in\mathbb{N}$ such that every…

Let $K,n \in \mathbb{N}$. A graph has a $K$-fat $(n\times n)$-grid minor if it contains the corresponding fat minor model, and graphs are $(M,A)$-quasi-isometric when they satisfy…