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SUMMARY:Michelle Delcourt (Ryerson)
DTSTART:20220202T140000Z
DTEND:20220202T150000Z
DTSTAMP:20260423T003234Z
UID:WCS/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WCS/46/">Rec
 ent Progress on Hadwiger's Conjecture</a>\nby Michelle Delcourt (Ryerson) 
 as part of Warwick Combinatorics Seminar\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 a recent breakthrough\, Norin\, Song\, and Postle pr
 oved that every graph with no $K_t$ minor is $O(t (\\log t)^c)$-colorable 
 for every $c > 0.25$\,  Subsequently Postle showed that every graph with n
 o  $K_t$ minor is $O(t (\\log \\log t)^6)$-colorable. We improve upon this
  further showing that every graph with no $K_t$ minor is $O(t \\log \\log 
 t)$-colorable. Our main technical result yields this as well as a number o
 f other interesting corollaries. A natural weakening of Hadwiger's Conject
 ure is the so-called Linear Hadwiger's Conjecture that every graph with no
  $K_t$ minor is $O(t)$-colorable.  We prove that Linear Hadwiger's Conject
 ure reduces to small graphs as well as that Linear Hadwiger's Conjecture h
 olds for the class of $K_r$-free graphs (provided $t$ is sufficiently larg
 e). This is joint work with Luke Postle.\n
LOCATION:https://researchseminars.org/talk/WCS/46/
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