A little more generally, the unipolar graphs are the graphs that can be partitioned into a clique and a cluster graph, a disjoint union of cliques. These include, for instance, the complements of bipartite graphs, as they can be partitioned into two cliques. The unipolar graphs and their complements together form the class of generalized split graphs. Almost all perfect graphs are generalized split graphs, in the sense that the fraction of perfect n-vertex graphs that are generalized split graphs goes to one in the limit as n grows arbitrarily large.
