Depth difference between a fullerene and its dual

Prove or disprove that every fullerene graph $F$ satisfies $|d(F)-d(F^*)|\le 2$, where $F^*$ is the planar dual and $d$ denotes asymmetric depth.

Background

The paper observes examples in which the asymmetric depths of a fullerene and its dual are equal, as well as examples in which either one is larger. Exhaustive computations for fullerenes through 118 vertices found an absolute difference of at most 2, motivating the stated conjecture.

References

We conjecture that for every fullerene graph $F$, $|d(F) - d(F*)| \le 2$.

— Extremal Asymmetric Depth of Planar Graphs and Hidden Near-Mirror Symmetries of IPR Fullerenes  (2609.02585 - Pastorek, 2 Sep 2026) in Section 7, “Concluding remarks”