Speaker: Tuan Tran, Specially Appointed Professor (tenured) at the University of Science and Technology of China

Date: November 11, 2022

Time: 16:00-17:00

Location: Zoom

Sponsor: School of Mathematics, Shandong University

Abstract:

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.

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https://www.view.sdu.edu.cn/info/1020/171919.htm