6 problems

List distinguishing index conjecture.

Linear list-assignment conjecture. There is a function $\delta_2:\mathbb{N}\times(0,+\infty)\ni(\ell,\varepsilon)\to\mathbb{R}$ such that $\delta_2=O(\ell\varepsilon^{-1})$ and, fo…

List strengthening conjecture. For every integer $k\geq 2$, if a graph $G$ has minimum degree $\delta(G)\geq k^2$, then $G$ has a $1/k$-majority edge colouring from any lists of si…

Balanced list-colouring reconfiguration conjecture. If $\operatorname{mad}(G)=d$ and

List Colouring Reconfiguration Conjecture. If

List-homomorphism product conjecture. Then