On Independent Complete Subgraphs in a Graph

Source abstract

A graph G = G(n, e) consists of a set of n nodes e pairs of which are joined by a single edge; we assume that no edge joins a node to itself. A graph with modes is called a complete -graph if each pair of its nodes is joined by an edge. The graphs belonging to some collection of graphs are independent if no two of them have a node in common. The maximum number of independent complete -graphs contained in a given graph G will be denoted by I k (G) .