With just considering the number of edges that meet at a vertex, prove that f >= 2 + 1/3(e)
So what I have is that a polyhedron is 3D so at least 3 edges will meet at each vertex, that's equivalent to its degree. Since the sum of all vertex totals = 2e then 3v =< 2e
Then since a polyhedron is a plane graph, we can use V - E + F = 2 => F = 2 - V + E
But using all of the above I got f >= 2 - (-2/3)v + e = 2 + 5/3(e), which is not what it should be.
Where did I make an incorrect assumption? Thanks!
I'm thinking my error is in assuming v =< 2/3 (e) is equal to v >= -2/3(e)...