3 problems

Let the directed triangle mean the cyclic tournament on three vertices, and say that a tournament has the Strong Erdős–Hajnal property when it satisfies the strong Erdős–Hajnal con…

Let $T$ be a tournament, let $D$ be a simple digraph on $n$ vertices with no subdigraph isomorphic to $T$, and let $\vec{\alpha}(D)$ denote its largest acyclic set. Strong Erdős–Ha…

Let $H$ be a graph. A set of vertices $A$ is complete to a disjoint set $B$ if every vertex of $A$ is adjacent to every vertex of $B$, and anti-complete if no such edges exist. Str…