- This event has passed.

# Shengtong Zhang (张盛桐), Triangle Ramsey numbers of complete graphs

## Tuesday, December 19, 2023 @ 4:30 PM - 5:30 PM KST

Room B332,
IBS (기초과학연구원)

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 involves a combination of results on the chromatic number of triangle-sparse graphs.

Joint work with Jacob Fox and Jonathan Tidor.