4 problems

Relative rainbow Turán conjecture for hypercubes. The hypercube has the property that

Weighted rainbow clique conjecture. If $n\ge r$, $G_0$ contains no $K_r$ with weight sequence bound $(1,2,\ldots,\binom{r}{2})$, then: (i) if $k=k_1$,…

Keevash–Saks–Sudakov–Verstraëte quadratic-range conjecture. The exact formula and extremal-structure conclusion for $\operatorname{ex}_k(n,K_r)$ established for sufficiently large…

Keevash–Saks–Sudakov–Verstraëte conjecture. Suppose $k\ge h$ and $n$ is sufficiently large. Then