1. The problem statement, all variables and given/known data Show that if every region in a planar graph has an even number of bounding edges, then the vertices can be 2-colored. 3. The attempt at a solution So i think it would suffice to show that if that all the regions have an even number of boundary edges, then, a complete circuit with even length must exist. But i dont know if thats true or how to prove it. Any help is appreciated.