Improved bound for Hadwiger's conjecture

Published 20 Aug 2021 in math.CO | (2108.09230v1)

Abstract: 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.}