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
Clique and anticlique partitions of graphs
✍ Scribed by Krzysztof Bryś; Zbigniew Lonc
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 408 KB
- Volume
- 185
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
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.
📜 SIMILAR VOLUMES
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
Let To denote the complement of a perfect matching in the complete graph on v vertices, v even, and let cp(To) be the minimum number of cliques needed to partition the edge-set of To. We prove that cp(To)>-v for v 1> 8 and give a design characterization of the cases where equality holds. We also sho
We consider the following generalization of split graphs: A graph is said to be a (k; ')-graph if its vertex set can be partitioned into k independent sets and ' cliques. (Split graphs are obtained by setting k = ' = 1.) Much of the appeal of split graphs is due to the fact that they are chordal, a
Wallis, W.D. and G.-H. Zhang, On the partition and coloring of a graph by cliques, Discrete Mathematics 120 (1993) 191-203. We first introduce the concept of the k-chromatic index of a graph, and then discuss some of its properties. A characterization of the clique partition number of the graph G V