Hadwiger's conjecture for graphs with infinite chromatic number
  We construct a connected graph H such that (1) \chi(H) = \omega; (2) K_\omega, the complete graph on \omega points, is not a minor of H. Therefore Hadwiger's conjecture does not hold for graphs with infinite coloring number. 
Dominic van der Zypen
math.CO cs.DM math.LO