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Matija Bucić, Essentially tight bounds for rainbow cycles in proper edge-colourings
Tuesday, October 17, 2023 @ 4:30 PM - 5:30 PM KST
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
A 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.
Joint work with: Noga Alon, Lisa Sauermann, Dmitrii Zakharov and Or Zamir.