[peterderivaz]

Not the original poster, but one thing that confused me was that I can clearly draw a graph that cannot be two coloured with a single pen stroke if I am allowed to reverse direction and keep drawing back over the same line again (indeed it is of course possible to draw any connected graph this way). I wasn't sure which part of the conditions forbid this.

Perhaps it is no longer a graph if I have a bidirectional edge? Or perhaps it is not considered planar if two edges coincide?

[ColinWright]

Ah, it's not allowed to go back exactly over the same line, so you can't reverse direction. You can go back and revisit the same node, but it will require a separate edge, and the two parts of the stroke will then encompass another area.

I'll add that - thanks!

Edit: now added - it will go live when the page updates.