2 problems

The extremal $K_4$-free graph conjecture. For $n\ge 10$, the $n$-vertex graph not containing $K_4$ that maximizes $\pi_f$ is $K_{1,\lfloor (n-1)/2\rfloor,\lceil (n-1)/2\rceil}$. Th…

Let $G$ be a bipartite graph on $n$ vertices. Write $K_{\lfloor n/2\rfloor,\lceil n/2\rceil}$ for the complete bipartite graph whose parts have sizes $\lfloor n/2\rfloor$ and…