Title：Balanced subdivisions of cliques in graphs

Abstract：In 1984, Thomason conjectured that for each integer k≥1, high average degree is sufficient to guarantee a balanced subdivision of K_k. Recently, Liu and Montgomery resolved this conjecture. We give an optimal estimate up to an absolute constant factor by showing that there exists c>0 such that for sufficiently large d, every graph with average degree at least d contains a balanced subdivision of a clique with at least cd^(1/2) vertices. It also confirms a conjecture from Verstraëte: every graph of average degree cd^2, for some absolute constant c > 0, contains a pair of disjoint isomorphic subdivisions of graph K_d.Speaker：Guanghui Wang is the professor and secretary of the Party committee of School of Mathematics, Shandong University. Winner of Shandong Outstanding Youth Fund, vice chairman and secretary general of Graph Theory and Combinatorics Branch of ORSC. He is mainly interested in the Combinatorial Mathematics and its application in Data Science and other fields, and has published more than 40 papers in SCI academic journals such as Journal of London Mathematical Society，ACM-SIAM Symposium on Discrete Algorithms(SODA)， Journal of Graph Theory, European Journal of Combinatorics and Combinatorics Probability & Computation.  

Date：9:00am-11:00am 2022-5-13（Friday）.

Tencent Meeting ID： 389-530-887

Organizer：School of Mathematical Science

Students and teachers who are interested in graph theory are welcome.