Figure 1.

Graphs with three (A) and six (B) vertices. The largest subgraph that forms a clique in A is {1,2,3} and in B, {1,3,4,5,6}. We denote these subgraphs with the vertices they contain. For example, {1,3} denotes the subgraph that contains vertices 1 and 3. For simplicity, we use the terms subgraph and subset interchangeably in this paper (formally, a subset is a collection of vertices of a graph G, and a subgraph is a collection of vertices and edges of G).