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zzzzz
Posts:
2
Registered:
6/4/06


Graph theory
Posted:
Jun 4, 2006 1:32 AM


(i).
Let G be a simple connected cubic plane graph, and let phi_k be the number of ksided 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
(ii).
Deduce that G has at least one face bounded by at most five edges



