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DTSTART:20190101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200917T100000
DTEND;TZID=Asia/Seoul:20200917T110000
DTSTAMP:20260424T063550
CREATED:20200811T231948Z
LAST-MODIFIED:20240707T082734Z
UID:2789-1600336800-1600340400@dimag.ibs.re.kr
SUMMARY:Luke Postle\, Further progress towards Hadwiger's conjecture
DESCRIPTION:In 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 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 no $K_t$ minor is $O(t(\log t)^{\beta})$-colorable for every $\beta > 1/4$\, making the first improvement on the order of magnitude of the $O(t\sqrt{\log t})$ 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 are $O(t (\log \log t)^{6})$-colorable.
URL:https://dimag.ibs.re.kr/event/2020-09-17/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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