The Euler Characteristic
V are the vertices, E are the edges and F are the faces.
V = _____ F = ______ E = ______
V = _____ F = ______ E = ______
V = _____ F = ______ E = ______
Draw your own network, the edges cannot cross.
V = _____ F = ______ E = ______
Once you see the pattern, can you draw a network with 5 vertices where all the vertices are connected
to all the other vertices? How many edges would there have to be? How many edges would bound a
face?
How about a complete graph with 4 vertices?
Can you prove that 4 is the biggest complete planar graph you can draw?
Now let’s do the 3 well problem.
Can you inductively prove the Euler Characteristic?