5 problems

Let $J$ be a finite graph and let $K\in\mathbb N$. A graph has no $K$-fat $J$ minor if it contains no geometric $J$ minor whose branch sets and connecting paths are mutually at dis…

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 $K,d\in\mathbb{N}$, and let $H$ be a graph. A graph forbids a $K$-fat $H$ minor if it contains no such fat minor model. Then there exist some $M,A\in\mathbb{N}$ and a graph…

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…