2 problems

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Grünbaum's conjecture on spanning trees and co-trees of planar graphs
Grünbaum's conjecture. Every planar 3-connected graph $G$ contains a 3-tree $T$ whose co-tree $\neg T^*$ is also a 3-tree.
Conjectureopengraph-duality planar-graphs spanning-treesarXiv posted 2 days ago
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Wilson's conjecture on Class III regular maps
A regular map is a graph embedded in a surface with the regularity property that its automorphism group acts transitively on incident vertex-edge-face flags. A regular map is self-…
Conjectureopengraph-duality regular-maps ribbon-graphsarXiv posted 2 days ago

Grünbaum's conjecture on spanning trees and co-trees of planar graphs