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DTSTART:20220101T000000
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DTSTART;TZID=Asia/Seoul:20231017T163000
DTEND;TZID=Asia/Seoul:20231017T173000
DTSTAMP:20260512T233525
CREATED:20230918T023401Z
LAST-MODIFIED:20240707T072941Z
UID:7670-1697560200-1697563800@dimag.ibs.re.kr
SUMMARY:Matija Bucić\, Essentially tight bounds for rainbow cycles in proper edge-colourings
DESCRIPTION:An edge-coloured graph is said to be rainbow if it uses no colour more than once. Extremal problems involving rainbow objects have been a focus of much research over the last decade as they capture the essence of a number of interesting problems in a variety of areas. A particularly intensively studied question due to Keevash\, Mubayi\, Sudakov and Verstraëte from 2007 asks for the maximum possible average degree of a properly edge-coloured graph on n vertices without a rainbow cycle. Improving upon a series of earlier bounds\, Tomon proved an upper bound of $(\log n)^{2+o(1)}$ for this question. Very recently\, Janzer-Sudakov and Kim-Lee-Liu-Tran independently removed the $o(1)$ term in Tomon’s bound. We show that the answer to the question is equal to $(\log n)^{1+o(1)}$.\nA key tool we use is the theory of robust sublinear expanders. In addition\, we observe a connection between this problem and several questions in additive number theory\, allowing us to extend existing results on these questions for abelian groups to the case of non-abelian groups.\nJoint work with: Noga Alon\, Lisa Sauermann\, Dmitrii Zakharov and Or Zamir.
URL:https://dimag.ibs.re.kr/event/2023-10-17/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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