1. Is it possible to remove some edges from the complete graph K9 so that the degree of each vertex is equal to 6? Explain your answer. 2. For which values of n, m is the graph Kn,m planar? Explain your answer. 3. For what minimum n, if you color each edge of the complete graph Kn red or blue, you are guaranteed to get a triangle of the same color (a monochromatic triangle)? Explain your answer. 4. Is it possible to draw a given graph without lifting a pencil? Explain your answer.