3 problems

Baker–Rumely's lower bound conjecture. There is a universal constant $C>0$ such that, for every metrized graph $\Gamma$,

Let $\Gamma$ be a metrized graph, let $\tau(\Gamma)$ denote its tau constant, and let $\ell(\Gamma)$ denote its total length. Cinkir's explicit tau lower bound conjecture. For ever…

Let $\Gamma$ be a metrized graph, let $\ell(\Gamma)=\int_{\Gamma} dx$ be its total length, and consider metrized graphs with $\ell(\Gamma)\neq 0$. Baker and Rumely's tau lower boun…