7 problems

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

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

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…

Lidický–Murphy conjecture. There exist such integers for which

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…