5 problems

Gray-code canonical coloring conjecture. The canonical edge-coloring $\phi$ is an optimal strong parity edge-coloring of $P_n^\ell$.

For positive integers $r$, $t$, and $n$, let $P_n^t$ be the $t$-th power of the path on $n$ vertices, and let $R_<^r(P_n^t)$ denote the $r$-colour ordered Ramsey number of $P_n^t$.…

For positive integers $s$, $t$, and $n$, let $P_n^t$ be the $t$-th power of the path on $n$ vertices, let $K_s$ be the clique on $s$ vertices, and let $R_<(P_n^t,K_s)$ be their ord…

Let $P_n^t$ be the $t$th power of the ordered path on $n$ vertices, and let $K_n$ be the ordered complete graph on $n$ vertices. Write $R_{<}(G,H)$ for the ordered Ramsey number. P…

Let $P_n^t$ be the $t$th power of the ordered path on vertices $1,\ldots,n$, with edge set $\{(i,j):i<j\leq i+t\}$. Let $R_{<}(G,H)$ denote the ordered Ramsey number for graphs $G$…