9 problems

Wu–Zhang–Li conjecture. Graph $G$ is equitably vertex $k$-arborable whenever

Bounded-order list vertex arboricity conjecture. If

List colouring conjecture.

Let $G$ be a simple finite planar graph, and let $va^{\equiv}(G)$ denote its equitable vertex arborable threshold: the minimum integer $k$ such that $G$ admits an equitable tree-…

Planar equitable tree-3-coloring conjecture. Every planar graph is equitably tree-$3$-colorable; equivalently,

Planar equitable vertex arboricity conjecture. There exists a constant $k$ such that every planar graph is equitably tree-$k'$-colorable for every integer $k'\geq k$; equivalently,

Equitable Vertex Arboricity Conjecture. Every graph with maximum degree at most $\Delta$ is equitably tree-$k$-colorable for every integer $k\geq (\Delta+1)/2$; equivalently,

Let $G$ be a graph, let $\Delta(G)$ denote its maximum degree, and let $a^*_{eq}(G)$ be the smallest integer $t$ such that $G$ has an equitable $t'$-tree-coloring for every…

Let $G$ be a graph, let $\Delta(G)$ be its maximum degree, and let $va^{\equiv}_{\infty,\infty}(G)$ denote the strong equitable $(\infty,\infty)$-vertex-arboricity. Maximum-degree…