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? asked in Science & MathematicsMathematics · 1 decade ago

Each edge borders 2 faces, and every face has at least 3 edges -> 2E ≥ 3F?

This is a particular part of a proof that K5 (complete graph of 5 vertices) is not planar. And I don't see how to go from the left side of '->' to the right side. Can anyone explain this?

1 Answer

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  • jsjs
    Lv 5
    1 decade ago
    Favorite Answer

    Let's try to count the number of edges. Each face has at least 3 edges, so if we count three edges per face we get E ≥ 3F. However, this counts each edge twice, since each edge borders two different faces. Thus we have actually shown that 2E ≥ 3F.

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