Katona–Varga's generalized Kriesell conjecture

Let $t>0$, and let a minimally $t$-tough graph be a $t$-tough graph whose toughness decreases after deleting any edge. Katona–Varga's generalized conjecture. Every minimally $t$-tough graph has a vertex of degree $\lceil 2t\rceil$. The conjecture was disproved: Zheng and Sun (2024) found counterexamples for real $t$ close enough to $1$, and Cheng, Li, and Liu (2024) later gave new families of $4$-regular and $6$-regular counterexamples.