Katona and Varga showed that for any rational number $t \in (1/2,1]$, no chordal graph is minimally $t$-tough. We conjecture that no chordal graph is minimally $t$-tough for $t>1/2$ and prove several results supporting the conjecture. In particular, we show that for $t>1/2$, no strongly chordal graph is minimally $t$-tough, no split graph is minimally $t$-tough, and no chordal graph with a universal vertex is minimally $t$-tough.

翻译：Katona和Varga证明了对于任意有理数$t \in (1/2,1]$，不存在极小区$t$-tough的弦图。我们猜想对于$t>1/2$，不存在极小区$t$-tough的弦图，并证明了若干支持该猜想的结果。特别地，我们证明了对于$t>1/2$，不存在极小区$t$-tough的强弦图、不存在极小区$t$-tough的分裂图、且不存在包含泛化顶点的极小区$t$-tough弦图。