Clique partitions of the cocktail party graph

For our purposes, graphs have no loops or multiple edges. Aside from this, our terminology follows that of Bondy and Murty [1]. A clique is a complete subgraph. A clique partition of a graph G is a family ~ of cliques of G such that each edge of G is in precisely one member of q¢. The clique partition number, cp(G), is the minimum of the cardinalities of the clique partitions of G. Let To denote the graph on v = 2 n vertices ui, i = l , 2 , . . . , v with ui nonadjacent to ui+n for each i = 1, 2 , . . . , n. All other pairs of vertices are adjacent. This unique ( v 2)-regular graph on v vertices is called the cocktail party graph.