**Conjecture**Suppose with is a connected cubic graph admitting a -edge coloring. Then there is an edge such that the cubic graph homeomorphic to has a -edge coloring.

Reformulation via 4-flows:

**Conjecture**Suppose is a cubic graph with a nowhere-zero -flow, then there is an edge such that has a nowhere-zero -flow.

## Bibliography

* indicates original appearance(s) of problem.