3 problems

Let $D$ be a strong digraph with $n$ vertices. A pair is dominated or dominating when it is a pair of dominated or dominating nonadjacent vertices of $D$ as specified in the source…

Let $G$ be a 3-edge-connected simple graph of order at most $17$, let $\mathcal{SL}$ denote the class represented by \text{cal S!L}, and let $P$, $P_{14}$, and $P_{16}$ be the…

Let $G$ be a 3-edge-connected nontrivial reduced graph, and let $F(G)$ denote its $F$-value. Let $P$ denote the Petersen graph. Catlin's conjecture. If $F(G)=3$, then $G$ must be…