$K_4^{-}$-free triple systems without large stars in the complement

Dhruv Mubayi, Nicholas Spanier

The $n$-star $S_n$ is the $n$-vertex triple system with $\left(\genfrac{}{}{0ex}{}{n-1}{2}\right)$ edges all of which contain a fixed vertex, and $K_4^{-}$ is the unique triple system with four vertices and…