报告题目：Clique Subdivisions in Expanders

报告时间：5月23日3:30-4:30

报告人：Xingxing Yu, Georgia Institute of Technology,

地点：1218

摘要： A subdivision of a graph G is denoted T G. Mader conjectured that every C4-free graph with average degree d contains TK_l with l = Ω(d). Koml′os and Szemer′edi reduced this problem to expanders and proved Mader’s conjecture for n-vertex expanders with average degree d < exp(log1/8 n). We show that Mader's conjecture is true for n-vertex expanders with average degree d < n3/10, which improves Koml′os and Szemer′edi’s bound to a polynomial bound. As a consequence, we show that every C4-free graph with average degree d contains a TK_l with l = Ω(d/(log d) c ) for any c > 3/2. This is joint work with H. Huang and Y. Wang