BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Luke Postle (University of Waterloo)
DTSTART:20201126T020000Z
DTEND:20201126T030000Z
DTSTAMP:20260423T021020Z
UID:SCMSComb/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SCMSComb/21/
 ">Further progress towards Hadwiger's conjecture</a>\nby Luke Postle (Univ
 ersity of Waterloo) as part of SCMS Combinatorics Seminar\n\n\nAbstract\nI
 n 1943\, Hadwiger conjectured that every graph with no $K_t$ minor is $(t-
 1)$-colorable for every $t\\ge 1$. In the 1980s\, Kostochka and Thomason 
 independently proved that every graph with no $K_t$ minor has average degr
 ee $O(t\\sqrt{\\log t})$ and hence is $O(t\\sqrt{\\log t})$-colorable.  R
 ecently\, Norin\, Song and I showed that every graph with no $K_t$ minor i
 s $O(t(\\log t)^{\\beta})$-colorable for every $\\beta > 1/4$\, making the
  first improvement on the order of magnitude of the $O(t\\sqrt{\\log t})$ 
 bound. Here we show that every graph with no $K_t$ minor is $O(t (\\log t)
 ^{\\beta})$-colorable for every $\\beta > 0$\; more specifically\, they ar
 e $O(t (\\log \\log t)^{6})$-colorable.\n\npw 121323\n
LOCATION:https://researchseminars.org/talk/SCMSComb/21/
END:VEVENT
END:VCALENDAR