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
Graph partition into small cliques
β Scribed by Yan, Jin; Gao, Yunshu; Zhang, Beibei
- Book ID
- 122808465
- Publisher
- Elsevier Science
- Year
- 2014
- Tongue
- English
- Weight
- 419 KB
- Volume
- 162
- Category
- Article
- ISSN
- 0166-218X
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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
It is shown in this note that it can be recognized in polynomial time whether the vertex set of a finite undirected graph can be partitioned into one or two independent sets and one or two cliques. Such graphs generalize bipartite and split graphs and the result also shows that it can be recognized