4 problems

For a tournament $T$ and an ordering $\prec$ of $V(T)$, let $T^{\prec}$ be its backedge graph. A BST-ordering is the ordering associated with a binary search tree satisfying the to…

Let $P_{n_1}$ denote the path on $n_1$ vertices and $K_{n_2}$ the complete graph on $n_2$ vertices. For nonnegative integers $d_1,d_2$ and integers $n_1,n_2\geq 2$, write…

Let $P_n$ be the path on $n$ vertices, and consider all orderings of its vertices. Balko et al.'s conjecture. Among all orderings of $P_n$, the alternating path has minimum Ramsey…

Let $\mathcal{C}$ be a VR-equational class of graphs. Say that $\mathcal{C}$ has property $\mathsf{SEP}$ when it satisfies the separation property defined in the surrounding theory…