- Series
- Combinatorics Seminar
- Time
- Friday, September 6, 2024 - 3:15pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Shengtong Zhang – Stanford University – stzh1555@stanford.edu – https://sites.google.com/view/shengtong-zhang/
- Organizer
- Jiaxi Nie

A graph is $H$-Ramsey if every two-coloring of its edges contains a monochromatic copy of $H$. Define the $F$-Ramsey number of $H$, denoted by $r_F(H)$, to be the minimum number of copies of $F$ in a graph which is $H$-Ramsey. This generalizes the Ramsey number and size Ramsey number of a graph. Addressing a question of Spiro, we prove that \[r_{K_3}(K_t)=\binom{r(K_t)}3\] for all sufficiently large $t$.

Our proof employs many recent results on the chromatic number of locally sparse graphs. In particular, I will highlight a new result on the chromatic number of degenerate graphs, which leads to several intriguing open problems.