9 problems

DP-4-colorability conjecture. Every planar graph without chorded $6$-cycles is DP-$4$-colorable.

Let $G$ be a graph on $n$ vertices, and let $P^{*}_{DP}(G,k)$ denote its dual DP color function, the maximum number of colorings over all full $k$-fold covers of $G$. Dual-DP Shame…

Counting conjecture. For all sufficiently large $t$ and every $(k+t)$-fold cover $\mathcal{H}$ of $G\vee K_t$, the number of proper $\mathcal{H}$-colorings of $G\vee K_t$ is at lea…

Let $G$ be a triangle-free planar graph with $n$ vertices, and let $P_{DP}(G,4)$ denote its DP color function. The exponential DP-coloring conjecture. There exists a constant $c>1$…

Let $k$ be a power of a prime. For a graph $G$, let $P_{\mathcal{L}_k}(G,k)$ be the minimum number of colorings over all $\mathcal{L}_k$-labelings, where $\mathcal{L}_k$ is the col…

Cambie–Kang conjecture. For every $\varepsilon>0$, there is $d_0\in\mathbb{N}$ such that, if $H$ has maximum degree $d\geqslant d_0$ and

DP-version of the Alon–Krivelevich–Sudakov conjecture. For every graph $F$, there exist constants $c,d_0>0$ such that, whenever $H$ is $F$-free, has maximum degree $d\geqslant d_0$…

DP-coloring extension of the Alon–Krivelevich–Sudakov conjecture. For every graph $F$, there is a constant $c_F>0$ such that, if $H$ is $F$-free, has maximum degree $d\geqslant 2$,…

Let $G$ be a loopless multigraph, let $\Delta(G)$ denote its maximum degree, and let $\mathsf{Line}(G)$ be the simple graph whose vertices are the edges of $G$, with adjacency when…