(Solved): 4. Proper graph colorings Recall that a proper coloring of a graph is one where colors are given t ...

4. Proper graph colorings Recall that a proper coloring of a graph is one where colors are given to each vertex such that every pair of adjacent vertices have different colors. Shown below are the graphs K, (the complete graph on 5 vertices), C (the cycle graph on 5 vertices), and the Petersen graph. For each, determine the fewest colors one needs to properly color each and explain why fewer colors won't work. K? C5 Petersen graph