Problem 1. Is there a nonplanar graph which admits a 4-coloring? Justify your answer.
Problem 2. Prove that the graph shown in Figure 1 is nonplanar. (Hint: you can take it as given that there are no cycles of lengths 3 or 4 in this graph).
Figure 1: The graph referenced in Problems 2 and 3.
Problem 3. What Is the chromatic number of the graph shown in Figure 1? Justify your answer.