11 problems

Postle–Smith-Roberge correspondence-colouring conjecture. If $|L(v)|\geq \max\{3,8-g(v)\}$ for every $v\in V(G)$, then $G$ is $(L,M)$-colourable.

Local girth correspondence-colouring hyperbolicity conjecture. There exists a theorem analogous to the paper's main hyperbolicity theorem for local girth correspondence colouring.

Local girth correspondence-colourability conjecture. If $G$ is a planar graph and $(L,M)$ is a correspondence assignment for $G$ where $L$ is a local girth list assignment, then…

Langhede and Thomassen's conjecture. Planar graphs have exponentially many $5$-correspondence colourings.

For positive integers $a$ and $b$ with $a>b$, let $K_{a,b}$ denote the complete bipartite graph with parts of sizes $a$ and $b$, and let $\chi_c^\star$ denote its correspondence pa…

Let $G$ be a graph and let $v\in V(G)$. Vertex-deletion conjecture. Then … Equivalently, adding a new vertex adjacent to all existing vertices increases the correspondence packing…

Consider a group-partitioning problem with $n$ cohorts, each containing $k$ students, where for every student $S$ and every cohort $C$ not containing $S$ there is at most one stude…

Kr-free correspondence-cover packing conjecture. For every $r\ge3$, there is some $C_r>0$ such that the following holds for

Bipartite correspondence-cover packing conjecture. There is some $k=k(\Delta)$ satisfying

Independent-transversal packing conjecture.

Triangle-free correspondence packing conjecture.