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Given a planar graph G such that all the vertices have even degrees: Prove that...

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Algebra

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Given a planar graph G such that all the vertices have even degrees: Prove that all theregions separated out by this graph (all the faces) can be 2-colored. That is, the faces canbe colored such that no two faces which share an edge can have same color. (Hint: Useinduction. Look at outer rim of the graph and think about removing all the edges of theouter rim.)

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