Hadwiger’s Conjecture

Hadwiger’s Conjecture from 1943 states that for every integer t
greater than or equal to 1, every graph either can be t-colored or has
a subgraph that can be contracted to the complete graph on t plus 1
vertices. This is a far-reaching generalization of the Four-Color
Theorem and perhaps the most famous conjecture in graph theory. Until
recently the best known upper bound on the chromatic number of graphs
with no Kt minor is O(t (log t)^1/2), obtained independently by
Kostochka and Thomason in 1984, while joint with Norin and Postle, we
improved the frightening (log t)^1/2 term to (log t)^1/4 in 2019. The
current record is O(t log log t) due to Delcourt and Postle. In this
talk we will survey the history of Hadwiger’s Conjecture and discuss
some aspects of the proofs.
 

Bio
https://sciences.ucf.edu/math/zxsong/