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DTSTART;TZID=Asia/Seoul:20230316T100000
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SUMMARY:Paul Seymour\, A loglog step towards the Erdős-Hajnal conjecture
DESCRIPTION:In 1977\, Erdős and Hajnal made the conjecture that\, for every graph $H$\, there exists $c>0$ such that every $H$-free graph $G$ has a clique or stable set of size at least $|G|^c$; and they proved that this is true with $|G|^c$ replaced by $2^{c\sqrt{\log |G|}}$. \nThere has no improvement on this result (for general $H$) until now\, but now we have an improvement: that for every graph $H$\, there exists $c>0$ such that every $H$-free graph $G$ with $|G|\ge 2$ has a clique or stable set of size at least $$2^{c\sqrt{\log |G|\log\log|G|}}.$$ This talk will outline the proof. \nJoint work with Matija Bucić\, Tung Nguyen and Alex Scott.
URL:https://dimag.ibs.re.kr/event/2023-03-16/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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