Clique coverings and partitions of line graphs Original Research Article

A clique in a graph image is a complete subgraph of image. A clique covering (partition) of image is a collection image of cliques such that each edge of image occurs in at least (exactly) one clique in image. The clique covering (partition) number image (image) of image is the minimum size of a clique covering (partition) of image. This paper gives alternative proofs, using a unified approach, for the results on the clique covering (partition) numbers of line graphs obtained by McGuinness and Rees [On the number of distinct minimal clique partitions and clique covers of a line graph, Discrete Math. 83 (1990) 49–62]. We also employ the proof techniques to give an alternative proof for the De Brujin–Erdős Theorem.