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Halfway to Hadwiger's Conjecture
In 1943, Hadwiger conjectured that every -minor-free graph is
-colorable for every . In the 1980s, Kostochka and Thomason
independently proved that every graph with no minor has average degree
and hence is -colorable. Very recently,
Norin and Song proved that every graph with no minor is -colorable. Improving on the second part of their argument, we
prove that every graph with no minor is -colorable
for every .Comment: 16 page