i'm stuck on this proof:
prove that any planar graph with very vertex having degree 5 has at least 12 vertices.
a planar graph G with all v vertices with degree 5 has 5v/2 edges
Euler's formula states that vertices - edges + faces = 2
so there are 3v/2 + 2 faces in G
I'm not sure how to get the # of faces in G, or whether it's relevant to the problem.
also this one:
show that a plane graph with v>=3 vertices has at most 2v - 4 edges
any help is appreciated.