2 problems

For a finite graph $G$, let $c_1^+(G)$ denote the supremum of the flow-cut quantity over all nonnegative edge-length functions. For a family $\mathcal{F}$ of finite graphs, define…

Let $\mathcal{C}$ be a proper minor-closed family of graphs, and let $G=(V,E)$ be a connected graph in $\mathcal{C}$. Let $\operatorname{P_{\mathrm{sp.trees}}}(G)$ denote the conve…