一、题目：

Rainbow cycles in properly edge-colored graphs

二、主讲人：

Tuan Tran

三、摘要：

We prove that every properly edge-colored n-vertex graph with average degree at least 100(log n)2 contains a rainbow cycle, improving upon (log n)2+o(1) bound due to Tomon. We also prove that every properly colored n-vertex graph with at least 105k2n1+1/k edges contains a rainbow 2k-cycle, which improves the previous bound 2ck^2n1+1/k obtained by Janzer. Our method using homomorphism inequalities and a lopsided regularization lemma also provides a simple way to prove the Erdős-Simonovits supersaturation theorem for even cycles, which may be of independent interest. Joint work with Jaehoon Kim, Jookyung Lee, Hong Liu.

四、主讲人简介：

Tuan Tran is a Specially Appointed Professor (tenured) at University of Science and Technology of China, where he is a member of the Combinatorics Group. Previously, he was a Young Scientist Fellow at Institute for Basic Science (IBS). He got his PhD in 2015 from Free University of Berlin. His research interests include extremal and probabilistic combinatorics, ramsey theory, additive combinatorics, and discrete geometry.

五、邀请人：

王光辉 数学学院教授

六、时间：

11月11日（周五）16:00-17:00

七、地点：

腾讯会议

八、联系人：

常渝林，联系方式：ylchang@sdu.edu.cn

九、主办：

山东大学数学学院