Las Vergnas–Meyniel conjecture on Kempe equivalence and graph minors

For a graph $G$, a $t$-colouring is a proper colouring using $t$ colours, and two colourings are Kempe equivalent when they are connected by a sequence of Kempe changes, each swapping two colours on a maximal bichromatic component. Let $K_t$ denote the complete graph on $t$ vertices, and say that $G$ has no $K_t$-minor when it does not contain $K_t$ as a graph minor. Las Vergnas–Meyniel's Conjecture A. For every $t$, all the $t$-colourings of a graph with no $K_t$-minor form a single equivalence class. The paper states that this conjecture is disproved by its construction of graphs with no $K_t$-minor having non-equivalent colourings.