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TZOFFSETFROM:+0900
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DTSTART:20230101T000000
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DTSTART;TZID=Asia/Seoul:20241008T163000
DTEND;TZID=Asia/Seoul:20241008T173000
DTSTAMP:20260415T195816
CREATED:20240815T140405Z
LAST-MODIFIED:20240815T140630Z
UID:9708-1728405000-1728408600@dimag.ibs.re.kr
SUMMARY:Mathias Schacht\, Canonical colourings in random graphs
DESCRIPTION:Rödl and Ruciński established Ramsey’s theorem for random graphs. In particular\, for fixed integers $r$\, $\ell\geq 2$ they showed that $n^{-\frac{2}{\ell+1}}$ is a threshold for the Ramsey property that every $r$-colouring of the edges of the binomial random graph $G(n\,p)$ yields a monochromatic copy of $K_\ell$. \nWe investigate how this result extends to arbitrary colourings of $G(n\,p)$ with an unbounded number of colours. In this situation Erdős and Rado showed that canonically coloured copies of $K_\ell$ can be ensured in the deterministic setting.\nWe transfer the Erdős-Rado theorem to the random environment and show that for $\ell\geq 4$ both thresholds coincide. As a consequence the proof yields $K_{\ell+1}$-free graphs $G$ for which every edge colouring yields a canonically coloured $K_\ell$. \nThis is joint work with Nina Kamčev.
URL:https://dimag.ibs.re.kr/event/2024-10-08/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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