Hadwiger conjectured in 1943 that for every integer $t ge 1$, every graph with no $K_t$ minor is $(t-1)$-colorable. Kostochka, and independently Thomason, proved every graph with no $K_t$ minor is $O(t(log t)^{1/2})$-colorable. Recently, Postle improved it to $O(t (log log t)^6)$-colorable. In this paper, we show that every graph with no $K_t$ minor is $O(t (log log t)^{5})$-colorable.
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