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Hadwiger's conjecture for graphs with infinite chromatic number

Published 13 Dec 2012 in math.CO, cs.DM, and math.LO | (1212.3093v1)

Abstract: 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.

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