I'm trying to understand the concept of nowhere-zero-flows.
I have this example graph that's supposed to have a nowhere-zero-4-flow (since it has a Hamiltonian cycle).
So by one of the theorems by Tutte, it should also have a nowhere-zero $\mathbb{Z}_2 \times \mathbb{Z}_2$-flow.
If I understood it correctly, the flows assigned to the edges need to have a value out of $\{(0,1), (1,0), (1,1)\}$ and have to sum up to an even number.
For some reason I don't manage to assign the flows correctly. Help would be appreciated!
Take an entirely clockwise orientation; label all edges outside the triangle $(1,1)$, and label the edges of the triangle $(0,1)$ and $(1,0)$ accordingly.
There are of course many variations on this solution.