Abstract
A clique in a graph G is a complete subgraph of G . A clique covering ( partition) of G is a collection C of cliques such that each edge of G occurs in at least (exactly) one clique in C . The clique covering ( partition) number cc ( G ) ( cp ( G ) ) of G is the minimum size of a clique covering (partition) of G . 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.
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