Havet–van den Heuvel–McDiarmid–Reed planar square list-coloring conjecture

Let $G$ be a planar graph. Havet–van den Heuvel–McDiarmid–Reed conjecture.

$$\chi_{\ell}^2(G)=\chi^2(G).$$

The conjecture was disproved in 2022 by Hasanvand, although it remains open for graphs with maximum degree at least $4$.