Surface construction for oriented 9-cycle 6-covers

Determine whether it is possible to glue an orientable surface from the circuits of an oriented 9-cycle 6-cover.

Background

The paper surveys known existence results for ordinary and oriented cycle covers with sixfold edge coverage. It notes that oriented 9-cycle 6-covers exist for several small snarks and asks whether the surface-gluing techniques developed for oriented 6-cycle 4-covers extend to oriented 9-cycle 6-covers.

References

It also seems possible to introduce notions of poor and rich edges, as well as ordered and disordered vertices, but we haven't found anything interesting stuff here for now, as well as we don't know, whether it's possible to glue any kind of surface out of the o9c6c circuits.

— Computational Graph Decompositions I: Oriented Berge-Fulkerson Conjecture  (2501.05348 - Ulyanov, 9 Jan 2025) in Section “6-covers”