On a recolouring version of Hadwiger's conjecture

Marthe Bonamy, Marc Heinrich, Clément Legrand-Duchesne, Jonathan Narboni

Abstract: We prove that for any ε>0, for any large enough t, there is a graph that admits no Kt-minor but admits a (32−ε)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.