4 problems

Let $T=(A,\succ)$ be a tournament, and let $\operatorname{TEQ}$ denote the tournament equilibrium set. A nonempty subset $X\subseteq A$ is TEQ-retentive if…

Let $T$ be a tournament and let $R\subseteq V(T)$ be a minimal TEQ-retentive set with $|R|=3$. Size-three uniqueness conjecture. Then $R$ is the unique minimal TEQ-retentive set of…

Let $T$ be a tournament. A captain vertex is a vertex with the captain property used in the paper, and let $A$ be the set of all captain vertices of $T$. Captain inclusion conjectu…

Let $T$ be a tournament, and let $\mathfrak{Dom}(T)$ denote its directed domination graph. A set is TEQ-retentive when it satisfies the tournament-equilibrium-set retentiveness con…