 
Summary: Theorem
Suppose we have a simple connected planar graph.
Let V be the number of vertices and E the number of edges.
Then 3V  6 E.
Let's pretend our graph is the floor plan of a house.
So each "room," counting the outside, is a face.
Suppose you have to paint the walls (inside and out).
How many walls will you have to paint?
Let's pretend our graph is the floor plan of a house.
So each "room," counting the outside, is a face.
Suppose you have to paint the walls (inside and out).
How many walls will you have to paint?
Let's pretend our graph is the floor plan of a house.
So each "room," counting the outside, is a face.
Suppose you have to paint the walls (inside and out).
How many walls will you have to paint?
Let's pretend our graph is the floor plan of a house.
So each "room," counting the outside, is a face.
Suppose you have to paint the walls (inside and out).
How many walls will you have to paint?
