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Clique coverings and partitions of line graphs

✍ 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

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πŸ“œ SIMILAR VOLUMES


On the number of distinct minimal clique
✍ Sean McGuinness; Rolf Rees πŸ“‚ Article πŸ“… 1990 πŸ› Elsevier Science 🌐 English βš– 812 KB

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

Clique partitions and clique coverings
✍ Paul Erd'́os; Ralph Faudree; Edward T. Ordman πŸ“‚ Article πŸ“… 1988 πŸ› Elsevier Science 🌐 English βš– 575 KB

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

Clique and anticlique partitions of grap
✍ Krzysztof BryΕ›; Zbigniew Lonc πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 408 KB

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.

On clique partitions of split graphs
✍ W.D. Wallis; J. Wu πŸ“‚ Article πŸ“… 1991 πŸ› Elsevier Science 🌐 English βš– 204 KB

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