8 problems

Lv et al.'s conjecture. For $k\ge 4$ and sufficiently large $n$,

Lidický–Murphy conjecture. There exists a complete $(r-1)$-partite graph with asymptotically as many copies of $H$ as possible in a $K_r$-free graph, namely asymptotically…

Chen–Yang–Yuan–Zhang conjecture. For $n\geq 3k$ and $s\geq 3$,

Let $C_k$ denote a cycle on $k$ vertices, and let $\mathrm{ex}(n,T,F)$ be the maximum possible number of copies of a graph $T$ in an $F$-free graph on $n$ vertices. Erdős's conject…

Let $C_k^3$ and $P_k^3$ denote the edge blow-ups of the cycle $C_k$ and path $P_k$, respectively. For integers $p,t$, let $T_p(n-t+1)$ be the balanced $p$-partite complete graph on…

Let $G$ be a graph with diameter at most $2r-2$ and chromatic number $\chi(G)<r$. Diameter-bounded blow-up conjecture. The generalized Turán number $\operatorname{ex}(n,G,K_r)$ is…

Colored asymptotic sharpness conjecture.

For integers $k$ and $\ell$, write $\operatorname{ex}(n,C_k,C_\ell)$ for the maximum number of copies of the cycle $C_k$ in an $n$-vertex graph containing no copy of $C_\ell$. Let…