6 problems

Let $G$ be a planar graph, a triangle-free planar graph, or a planar graph of girth at least $5$, and let $L$ be a list assignment with respectively $10$, $7$, or $6$ colors on eac…

Let $G$ be a graph, let $L$ be a list assignment for which $L$-colorings are considered, and let $\mathcal{R}_L(G)$ be the graph whose vertices are the proper $L$-colorings of $G$,…

Cambie et al.'s conjecture. If

Cambie et al.'s conjecture. If

Let $G$ be a graph. A $4$-To-$3$ instance asks whether a proper $4$-coloring of $G$ can be transformed into a proper $3$-coloring by repeatedly recoloring one vertex while maintain…

Let $G$ be a graph and let $k$ be an integer with $k\geq 4$. A $k$-coloring of $G$ is a proper vertex coloring using colors from a set of $k$ colors, and $k$-Mixing asks whether an…