1. The graph coloring problem is the task of determining whether it is possible to color all the vertices in a graph such that no adjacent vertices have the same color, while using the minimum number of distinct colors. A greedy coloring algorithm is an algorithm for coloring a graph that iterates linearly through the graph's vertices in numeric order and assigns them the first available color. A color is considered available if no adjacent vertices have that color. The below pseudocode describes such an algorithm; in it, k represents the number of colors used, and adj(i) gives a list of all vertices adjacent to vertex i. # 1: function GREEDY-GRAPH-COLOR(G = (V, E) Assign a number i, 1k then k+ c(i) return k {c(j) jk then k+ c(i) return k {c(j) j