(Solved): Problem 3. (a) Determine the minimum number of colors needed to color the graph given below. The c ...

Problem 3. (a) Determine the minimum number of colors needed to color the graph given below. The complete solution must include: (i) A coloring with the appropriate number of colors, and (ii) a proof that it is not possible to use fewer colors. graph G b (b) Let H be a graph whose vertex degrees are 7, 7, 6, 6, 5, 4, 4, 4, 4, 3. Prove that H can be colored with 5 colors. (Note that there may be many graphs H with this degree sequence. Your proof must be valid for any such graph.)