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 K-t minor is (t - 1)-colorable. This is a strengthening of the famous Hadwiger's Conjecture. Geelen et al. proved that every graph with no odd K-t minor is O(t root logt)-colorable. Using the methods the present authors and Postle recently developed for coloring graphs with no K-t minor, we make the first improvement on this bound by showing that every graph with no odd K-t minor is O(t(logt)(beta))-colorable for every beta > 1/4.