We prove that for any $\varepsilon>0$, for any large enough $t$, there is a graph $G$ that admits no $K_t$-minor but admits a $(\frac32-\varepsilon)t$-colouring that is "frozen" with respect to Kempe changes, i.e. any two colour classes induce a connected component. This disproves three conjectures of Las Vergnas and Meyniel from 1981.

翻译：我们证明，对于任意 $\varepsilon>0$ 及任意足够大的 $t$，存在一个图 $G$，它不包含 $K_t$-子式，但允许一种 $(\frac32-\varepsilon)t$-着色方案，该方案相对于 Kempe 变换是“冻结”的，即任意两个颜色类诱导出一个连通分支。这一结论否定了 Las Vergnas 和 Meyniel 于 1981 年提出的三个猜想。