The ACO Seminar (2022–2023)

In 1954 Kővári, Sós and Turán showed that every $n$-vertex graph not containing $K_{s,t}$ has at most $O(n^{2-1/s})$ edges. We construct graphs matching this bound with $t\approx 9^s$, improving on factorial-type bounds. In this talk, I plan to give a high-level idea of the construction, and to share the sense of excitement by waving my hands a lot.