4 problems

Jacko–Jendrol conjecture. For every even $l\geq 8$,

Hexagonal-grid realization conjecture. The exact (maximal) value for each $n\in\mathbb{N}$ can be achieved in some hexagonal grid.

Let $G_{hex}$ be the infinite hexagonal grid. A firefighting strategy protects one vertex in each time unit, after which the fire spreads to all unprotected neighbors of burning ve…

Let $G_r$ be the finite hexagonal grid graph of radius $r$, let $V(G_r)$ be its vertex set, and let $N(W)$ and ${\mathscr E}(W)$ denote the relevant vertex and edge neighborhoods o…