A New Upper Bound on the Chromatic Number of Graphs with No Odd Kt Minor

Gerards and Seymour conjectured that every graph with no odd Kt minor is (t − 1)-colorable. This a strengthening of the famous Hadwiger’s Conjecture. Geelen et al. proved $$O(t\sqrt {\log t} )$$ -colorable. Using methods present authors Postle recently developed for coloring graphs minor, we make first improvement on this bound by showing O(t(logt)β)-colorable β > 1/4.