Subgraphs in multipartite graphs

Graph Theory Seminar
Tuesday, November 14, 2023 - 3:30pm for 1 hour (actually 50 minutes)
Skiles 006
Yi Zhao – Georgia State University – yzhao6@gsu.edu
Tom Kelly

In 1975 Bollobas, Erdos, and Szemeredi asked the following question: given positive integers $n, t, r$ with $2\le t\le r$, what is the largest minimum degree among all $r$-partite graphs G with parts of size $n$ and which do not contain a copy of $K_t$? The $r=t$ case has attracted a lot of attention and was fully resolved by Haxell and Szabo, and Szabo and Tardos in 2006. In this talk we discuss recent progress on the $r>t$ case and related extremal results on multipartite graphs.