(adsbygoogle = window.adsbygoogle || []).push({}); 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... :(

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# Homework Help: Graph theory, prove

Can you offer guidance or do you also need help?

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