3 problems

Let $P_\ell^+$ denote the expansion of a path $P_\ell$, and let $\mathcal{F}^*_{n,k,\ell}$ be the explicitly defined $P_\ell^+$-free family obtained from the star construction, wit…

Strengthened Erdős–Hajnal conjecture. For fixed $k\geq 4$,

Frankl–Jiang–Seiver conjecture. Analogous results, namely the corresponding extremal formulas and extremal-family descriptions, should hold for $k=3$.