5 problems

Peripheral-tree product conjecture.

Cartesian-product anti-van der Waerden conjecture.

Let $G$ be a graph with vertex set $V(G)$, and let $v\in V(G)$ be dominating if its closed neighborhood satisfies … For an integer $k\geq 3$, let $\operatorname{aw}(G,k)$ denote th…

Let $T$ be a tree, and let $\ell$ be a positive integer such that every path in $T$ contains at most $\ell$ bijacent vertices. Here, $\operatorname{aw}(T,3)$ denotes the anti-van d…

For a positive integer $n$, write $[n]=\{1,2,\ldots,n\}$, and let $\operatorname{aw}([n],3)$ be the smallest number of colors such that every exact coloring of $[n]$ with that many…