报告主题：Ramsey goodness of cycles

报 告 人：刘鸿教授

报告时间：2022年11月11日9:00--12:00

报告地点：腾讯会议ID：762-249-431

邀请单位：88038威尼斯、离散数学及其应用省部共建教育部重点实验室

报告摘要：

The Ramsey number R(F,H) is the minimum number N such that any N-vertex graph either contains a copy of F or its complement contains H. Burr in 1981 proved a pleasingly general result that for any graph H, provided n is sufficiently large, a natural lower bound construction gives the correct Ramsey number involving cycles: R(Cn,H)=(n−1)(χ(H)−1)+σ(H), where σ(H) is the minimum possible size of a colour class in a χ(H)-colouring of H. Allen, Brightwell and Skokan conjectured that the same should be true already when n≥|H|χ(H).

We improve this 40-year-old result of Burr by giving quantitative bounds of the form n≥C|H|log4χ(H), which is optimal up to the logarithmic factor. In particular, this proves a strengthening of the Allen-Brightwell-Skokan conjecture for all graphs H with large chromatic number.

This is joint work with John Haslegrave, Joseph Hyde, Jaehoon Kim.

报告人简介：

刘鸿教授2015在伊利诺伊大学厄本那-香槟分校取得博士学位，师从József Balogh。后于2019年在华威大学取得终身教职，并摘获英国科研创新未来领袖奖。于2022年加入韩国基础科学研究院任首席科学家，现是其极值及概率组合研究组的领头人。研究领域包括极值，概率组合，图论，离散几何，组合数论等。

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