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Topic: Graph theory
Replies: 1   Last Post: Jul 7, 2009 9:06 AM

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Posts: 2
Registered: 6/4/06
Graph theory
Posted: Jun 4, 2006 1:32 AM
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Let G be a simple connected cubic plane graph, and let phi_k be the number of
k-sided faces. By counting the number of vertices and edges of G, prove that:

3*phi_3 + 2*phi_4 + phi_5 - phi_7 - 2*phi_8 - . . . = 12


Deduce that G has at least one face bounded by at most five edges

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