The strong embedding conjecture for 2-connected graphs

A graph is 2-connected if it remains connected after deleting any one vertex. An embedding of a graph on a surface is a drawing with no two edges crossing; it is 2-cell if every face is homeomorphic to an open disk, and strong if every face boundary is a cycle of the graph.

Strong embedding conjecture. Every $2$-connected graph has a strong embedding on a surface.

This conjecture is stronger than the cycle double cover conjecture. It remains open for general graphs, although the cited theorem proves the cycle double cover conjecture for cubic graphs.