Disproof of the List Hadwiger Conjecture
  The List Hadwiger Conjecture asserts that every $K_t$-minor-free graph is $t$-choosable. We disprove this conjecture by constructing a $K_{3t+2}$-minor-free graph that is not $4t$-choosable for every integer $t\geq 1$. 
J\'anos Bar\'at, Gwena\"el Joret, David R. Wood
math.CO cs.DM