Show that a simple connected planar graph with 8 vertices and 13 edges cannot be bichromatic.

4. Draw a Complete Graph, Kn, with n > 4 that has a Hamiltonian Cycle but does not have an Eulerian Cycle. List the degrees of the vertices, draw the Hamiltonian Cycle on the graph and provide justification that there is no Eulerian Cycle.

You are given a simple graph. Prove that there must be at least two vertices with the same degree.

Show a simple disconnected graph with 6 vertices and 2 connected components.