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Math Help - Planar Graphs

  1. #1
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    Planar Graphs

    If G is a simple planar graph, does G contain a vertex of degree at most four? Prove or provide a counter example.

    Thanks!
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  2. #2
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    Re: Planar Graphs

    Quote Originally Posted by meggnog View Post
    If G is a simple planar graph, does G contain a vertex of degree at most four? Prove or provide a counter example.

    Thanks!
    Dear meggnog,

    No. The following simple planer graph has degree five in each vertex.
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    Last edited by Sudharaka; June 15th 2011 at 03:42 AM.
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