clique edge cover number | edge clique cover number | R-content

The intersection number ω(G), also called the edge clique cover number, clique edge cover number, R-content, or (confusingly) clique cover number, of a given graph G is the minimum number of cliques needed to cover all of the edges of G (i.e., whose edges form an edge cover of G). As a result of this definition, only maximal cliques need be considered. A connected graph G with vertex count n and edge count m satisfies ω(G)<=min(m, ⌊1/4 n^2⌋) (Harary 1994, pp. 19-20).

clique covering number | edge cover | Erdős sequence | graph intersection