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SUMMARY:Luke Postle (University of Waterloo)
DTSTART:20200914T140000Z
DTEND:20200914T150000Z
DTSTAMP:20260423T052450Z
UID:EPC/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EPC/23/">Fur
 ther progress towards Hadwiger's conjecture</a>\nby Luke Postle (Universit
 y of Waterloo) as part of Extremal and probabilistic combinatorics webinar
 \n\n\nAbstract\nIn 1943\, Hadwiger conjectured that every graph with no $K
 _t$ minor is $(t-1)$-colorable for every $t\\ge 1$. In the 1980s\, Kostoch
 ka and Thomason independently proved that every graph with no $K_t$ minor 
 has average degree $O(t\\sqrt{\\log t})$ and hence is $O(t\\sqrt{\\log t})
 $-colorable.  Recently\, Norin\, Song and I showed that every graph with n
 o $K_t$ minor is $O(t(\\log t)^{\\beta})$-colorable for every $\\beta > 1/
 4$\, making the first improvement on the order of magnitude of the $O(t\\s
 qrt{\\log t})$ bound. Here we show that every graph with no $K_t$ minor is
  $O(t (\\log t)^{\\beta})$-colorable for every $\\beta > 0$\; more specifi
 cally\, they are $O(t (\\log \\log t)^{6})$-colorable.\n
LOCATION:https://researchseminars.org/talk/EPC/23/
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