Question: Problem 3. Prove that any connected graph G (V,E) can be properly vertex-colored using at most IEI-IV| + 3 colors. (Hint: Since the graph is

Problem 3. Prove that any connected graph G (V,E) can be

Problem 3. Prove that any connected graph G (V,E) can be properly vertex-colored using at most IEI-IV| + 3 colors. (Hint: Since the graph is connected, it has a spanning tree. How many colors do you need to color just this spanning tree? Note that this may not be a proper coloring for the original graph. You need to modify this coloring so that the original graph can be colored properly.)

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