Clique coverings and partitions of line graphs

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 [11]. We also employ the proof techniques to give an alternative proof for the De Brujin-Erdos Theorem. Keywords. Clique, covering, partition, line graph, semiwing, wing, 3-wing.

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Bo-Jr Li, Gerard J. Chang
• Keywords: Alternative Proof, Clique, Complete Subgraph, DM 2008