Clique cover

Summary

In graph theory, a clique cover or partition into cliques of a given undirected graph is a collection of cliques that cover the whole graph. Generally, this means all vertices must be covered, and the term clique edge cover is used when all edges must be covered. A minimum clique cover is a clique cover that uses as few cliques as possible. The minimum $k$ for which a clique cover exists is called the clique cover number of the given graph.