Graph Theory and Combinatorics Seminar

Speaker: József Balogh (UIUC)

Title: Ramsey-Tur\'an type of Theorems in extremal graph theory

Abstract: S\'os in 1969 proposed a Ramsey variant of Tur\'an's theorem: what the maximum number of edges of a $K_r$-free graph with $n$ vertices which has $o(n)$ independence number?

Since then, Ramsey variants of several other classical extremal theorems were proved under the condition that the graphs have $o(n)$ independence number.

In this lecture we survey some of those results. Part of these results are due to Ce Chen, Bernard Lidicky,  Van Magnan, Grace McCourt, Andy McDowell, Hong Liu, Theo Molla, Richard Mycroft, Cory Palmer, Maryam Sharifzadeh.