  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.
