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$G$ is a planar graph, and all edges of $G$ are colored white or black. Prove that in any drawing of $G$ there exists a vertex $v$ such that going around the edges incident with $v$ in the clockwise direction, we encounter no more than two changes of color.

I think if I suppose this is not true, then I can find contradiction - there is a subgraph of $G$ which is isomorphic with $K_{3,3}$ - but it's just a idea. I really don't know how to solve.

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