A clique in a graph is a set of vertices all of which are pairwise adjacent. In other words, a clique of size \(n\) is just a copy of the complete graph \(K_n\text{.}\) We define the clique number of a graph to be the largest \(n\) for which the graph contains a clique of size \(n\text{.}\) Any clique of size \(n\) cannot be colored with fewer than \(n\) colors, so we have a nice lower bound:
in-context