Several new tools are presented for determining the number of cliques needed to (edge-)partition a graph. For a graph on n vertices, the clique partition number can grow end times as fast as the clique covering number, where c is at least 1/64. If in a clique on n vertices, the edges between cna vertices are deleted,1/2≤a≤1, then the number of cliques needed to partition what is left is asymptotic to c2n2a; this fills in a gap between results of Wallis for a≤1/2 and Pullman and Donald for a=1, c≥1/2. Clique coverings of a clique minus a matching are also investigated.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics