4. (Greedy Coloring Algorithm) The following psuedo-code that (allegedly) colors the ver tices of a graph so that no two adjacent vertices receive the same color. Such a coloring is called a vertex-coloring of G. Algorithm GCA Input: A simple undirected graph G with vertices V(G)-M,t, ,%). (The list of colors to be drawn from will be {1,2,... ,n]: GCA does not necessarily use all of these colors. Output: A vertex-coloring of G. For i 1 to n do L,-(1, . . . , i} (Li is the list of colors that may be assigned to For i- 1 to n do Set cthe first color in Li (ci is the color assigned to vi) For each j with i