Generalized Kriesell's conjecture for minimally tough graphs

Let $t$ be a real number, and let $G$ be a graph. A graph is minimally $t$-tough when $\tau(G)=t$ and $\tau(G-e)<t$ for every edge $e\in E(G)$, where $\tau(G)$ denotes its toughness. It is Generalized Kriesell's conjecture that every minimally $t$-tough graph has a vertex of degree $\lceil 2t\rceil$. This naturally generalizes Kriesell's conjecture for $t=1$, and the paper reports that the associated Kriesell conjecture was recently disproved.