Recall the definition of a complete graph K_n is a graph with n vertices such that every vertex is connected to every oilier vertex.

Recall also that a clique is a complete subset of some graph. The graph coloring problem consists of assigning a color to each of the vertices of a graph such that adjacent vertices have different colors and the total number of colors used is minimized.

We define the chromatic number of a graph G to be this minimum number of colors required to color graph G.

Prove that the chromatic number of a graph G is no less than the size of a maximal clique of G.