Mohar's APX-hardness conjecture for the genus of cubic graphs

A cubic graph is a graph in which every vertex has degree three. Mohar's conjecture. Approximating the genus of cubic graphs is APX-hard. This conjecture asserts computational hardness in the spherical-density regime, where graphs have average degree at most six; resolving the broader question of efficient constant-factor approximation in this regime is identified as a major open problem.