Clique coverings and partitions of line graphs
β Scribed by Bo-Jr Li; Gerard J. Chang
- Book ID
- 108113827
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 153 KB
- Volume
- 308
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let G be a line graph. Orlin determined the clique covering and clique partition numbers cc(G) and cp(G). We obtain a constructive proof of Orlin's result and in doing so we are able to completely enumerate the number of distinct minimal clique covers and partitions of G, in terms of easily calculab
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 et-? times as fast as the clique covering number, where c is at least l/64. If in a clique on n vertices, the edges between cn" ve
In the paper we prove that, for a fixed k, the problem of deciding whether a graph admits a partition of its vertex set into k-element cliques or anticliques (i.e. independent sets) is polynomial.
Wallis, W.D. and J. Wu, On clique partitions of split graphs, Discrete Mathematics 92 (1991) 427-429. Split graphs are graphs formed by taking a complete graph and an empty graph disjoint from it and some or all of the possible edges joining the two. We prove that the problem of deciding the clique