The clique cover problem (also sometimes called partition into cliques) is the problem of determining whether the vertices of a graph can be partitioned into k cliques.
It seems to me that a clique cover is defined as a set of cliques that partition the vertices of the graph.
An alternative definition of the intersection number of a graph G is that it is the smallest number of cliques in G (complete subgraphs of G) that together cover all of the edges of G. A set of cliques with this property is known as a clique edge cover or edge clique cover,
It seems to me that a clique edge cover is defined as a set of cliques that cover the vertices of the graph.
The two don't seem consistent to me. I searched in Douglas West's Introduction to Graph theory, Both clique cover and clique edge cover are defined in terms of cover instead of partition. So I wonder if the definition for clique cover in Wikipedia is wrong?