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Graph theory, prove

  1. Jan 31, 2010 #1
    1. The problem statement, all variables and given/known data

    If all vertices of planar graph have degrees greater than 4, prove if
    that graph has at least 12 vertices with degree of 5.

    2. Relevant equations

    d1+d2+...+dn= 2*m (m - number of edges, di-degree of i-vertex)
    f=2-n+m, f - number of faces, n-number of vertices

    3. The attempt at a solution

    I did this...
    2*m>= 12*5+(n-12)*6
    2*m>=3*f (every face defined with at least 3 edges, and every edge goes between 2 faces...)
    I'm not sure what to do next... :(
  2. jcsd
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