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Sat 22 Oct, 2005 09:31 pm
Let G be a simple graph with fewer than 12 faces, in which each vertex has degree at least 3.
(i). Use Euler's formula to prove that G has a face bounded by at most four edges.
(ii). Give an example to show that the result of part (i) is false if G has 12 faces.
I hope nobody answers your take-home exam for you.