- Series
- Graph Theory Seminar
- Time
- Tuesday, September 1, 2020 - 3:45pm for 1 hour (actually 50 minutes)
- Location
- https://bluejeans.com/681348075/????. (replace ???? with password) For password, please email Anton Bernshteyn (bahtoh~at~gatech.edu)
- Speaker
- Zhiyu Wang – Georgia Tech
- Organizer
- Anton Bernshteyn, Zhiyu Wang, and Xingxing Yu
A graph G is F-saturated if G is F-free and G+e is not F-free for any edge not in G. The saturation number of F, is the minimum number of edges in an n-vertex F-saturated graph. We consider analogues of this problem in other settings. In particular we prove saturation versions of some Ramsey-type theorems on graphs and Dilworth-type theorems on posets. We also consider semisaturation problems, wherein we only require that any extension of the combinatorial structure creates new copies of the forbidden configuration. In this setting, we prove a semisaturation version of the Erdös-Szekeres theorem on convex k-gons, as well as multiple semisaturation theorems for sequences and posets. Joint work with Gábor Damásdi, Balázs Keszegh, David Malec, Casey Tompkins, and Oscar Zamora.