# 3-Edge-Coloring Conjecture

**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.

### question

On June 22nd, 2022 Anonymous says:

wouldn't removing any edge from a cubic graph make the graph not cubic?

### A counterexample?

On August 3rd, 2021 Anonymous says:

What would be the cubic graph homeomorphic to K4-e? I think I can show there does not exist a cubic graph homeomorphic to K4-e. If so, this would seem to contradict the conjecture's claim.

### Is there yet any progress on this problem?

On November 13th, 2020 Anonymous says:

Hello, I would like to know whether anybody made any progress on this. I tried to google and found nothing. Also, why is there nothing in Bibliography of this problem? Is there any paper involving or proposing it? Thanks in advance

## Context

Is this conjecture missing some greater context? It seems obviously false on its own