8 problems

Linial–Morgenstern conjecture. For every tournament $T$, one has

Erdős's pentagon conjecture. For every triangle-free graph $G$,

For an $n$-vertex graph $G$, let $\mathrm{Obj}_{5,5}(G)$ be the number of $5$-vertex subsets inducing exactly $5$ edges, let $\mathrm{Obj}_{5,5}(n)$ be the maximum of this quantity…

Edge-Statistics Conjecture. The edge-inducibility constant satisfies

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 $d_{C_5}(p)$ denote the minimum possible density of copies of the 5-cycle $C_5$ in graphs with edge-density $p$. For an integer $k\geqslant 2$ and a real number…

Let $P_4$ be the path on four vertices, and let $3$-anti-common refer to the paper's rainbow-coloring property for three edge colors. Path anti-commonality conjecture. … Flag-algeb…

Let $G$ be a triangle-free graph of order $n$, and let $C_5$ denote the cycle of length five. A blow-up of $C_5$ is the graph obtained by replacing each vertex of $C_5$ with an ind…