3 Coloring Let G be an undirected graph. A coloring of G is an assignment of the numbers 1,.. ,r to the vertices in a way that the two end-points of any edge are colored with two distinct colors The greedy coloring algorithm considers the vertices in any order and assigns the smallest possible color to a vertex after examining the colors of its neighbors (those that have already been colored at this time For each of the following graphs, find how many colors the greedy algorithm uses in the worst case (a "bad" order , as a function of n or . Draw a small example graph illustrating this worst-case behavior (label the nodes with the resulting colors), and give a one-sentence explanation of how why this number of colors gets used