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Hadwiger conjectured in 1943 that every graph with no $K_t$ minor has chromatic number at most $t-1$. Delcourt and Postle proved that every graph with no $K_t$ minor has chromatic number $O(t\log\log t)$. We build on their result to improve this bound to $O(t\log\log\log t)$.
Asymptotic dimension of metric spaces is a large-scale analog of covering dimension of topological spaces. An intersection graph of a family of sets is the graph whose vertices are the members of the family and whose edges correspond to pairs of members with non-empty intersection. Our first main result connects the as...
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