8 problems

Let $G$ be a planar graph, and let $G^2$ denote its square, in which two vertices are adjacent when their distance in $G$ is at most two. Havet et al.'s conjecture. For any planar…

For a graph $G$, its square $G^2$ is the graph on $V(G)$ in which two vertices are adjacent when their distance in $G$ is at most two. Let $\chi$ and $\chi_\ell$ denote the chromat…

Cubic bipartite planar square-coloring conjecture. The square satisfies

Let $G$ be a graph. Its square $G^2$ is obtained by joining distinct vertices that are connected by a two-edge path in $G$. Let $\operatorname{\Delta}(G)$ be the maximum degree,…

For each positive integer $k$, let $\alpha_k$ be the minimum value such that there is a constant $c_k$ with … whenever $G$ is $k$-degenerate and has maximum degree at most $D$. Let…

Let $G$ be a planar graph with girth $5$, let $\Delta$ denote its maximum degree, and let $M$ be a constant. The Dvořák conjecture. There exists some constant $M$ such that every p…

Kostochka–Woodall conjecture.

List-colouring extension of Wegner's conjecture.