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Essentially tight bounds for rainbow cycles in proper edge-colourings

组织者

本杰明·苏达科夫

演讲者

Matija Bucic

时间

2024年03月12日 17:05 至 18:15

地点

Online

线上

Zoom 787 662 9899 (BIMSA)

摘要

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 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 $(\log n)^{(1+o(1))}$. Joint work with: Noga Alon, Lisa Sauermann, Dmitrii Zakharov and Or Zamir.

演讲者介绍

Matija Bucic is an Assistant professor in Mathematics at Princeton University. Before his current position, he studied at the University of Cambridge, received his PhD from ETH Zurich, and held a Veblen Research Instructorship, a joint position between IAS and Princeton. His research focuses on extremal and probabilistic combinatorics, as well as their applications to other areas of combinatorics and computer science.