# Local clique covering of graphs

Collaboration with Dr. Behnaz Omoomi and Zeinab Maleki.

A k-clique covering of a simple graph G, is an edge covering of G by its cliques such that

each vertex is contained in at most k cliques. The smallest k for which G admits a k-clique

covering is called local clique cover number of G. Local clique cover

number can be viewed as the local counterpart of the clique cover number which is equal to the

minimum total number of cliques covering all edges.