A graph is F-saturated if it is F-free but the addition of any edge creates a copy of F. In this talk, I will introduce the quantity sat(n,H,F) which denotes the minimum number of copies of H in an F-saturated graph on n vertices. This parameter is a natural saturation analog of Alon and Shikhelman’s generalized Tura’n problem, and letting $H=K_2$ recovers the well-studied saturation function. I will present a first investigation into this general function, focusing on the cases where the host graph is either $K_s$ or $C_k$-saturated. This is joint work with Abhishek Methuku, Michael Tait, and Craig Timmons.
Before the talk, at 3:10pm, there will be tea and cookies in Wean 6220.
The ACO Seminar (2018–2019)