The Tree-Width of Clique-Width Bounded Graphs without Kn,n
We proof that every graph of clique-width k which does not contain the complete bipartite graph Kn,n for some n > 1 as a subgraph has tree-width at most 3k(n - 1) - 1. This immediately implies that a set of graphs of bounded clique-width has bounded tree-width if it is uniformly l-sparse, closed under subgraphs, of bounded degree, or planar.
KeywordsPolynomial Time Tree Decomposition Complete Bipartite Graph Label Graph Graph Property
Unable to display preview. Download preview PDF.
- 3.B.D.G. Corneil, M. Habib, J.M. Lanlignel, B. Reed, and U. Rotics. Polynomial time recognition of clique-width at most three graphs. In Proceedings of Latin American Symposium on Theoretical Informatics (LATIN’ 2000), volume 1776 of LNCS. Springer-Verlag, 2000.Google Scholar
- 4.B. Courcelle, J.A. Makowsky, and U. Rotics. Linear time solvable optimization problems on graphs of bounded clique width, extended abstract. In Proceedings of Graph-Theoretical Concepts in Computer Science, volume 1517 of LNCS, pages 1–16. Springer-Verlag, 1998.Google Scholar
- 7.B. Courcelle. The monadic second-order logic of graphs XIV: Uniformly sparse graphs and edge set quantifications. submitted for publication, 2000.Google Scholar
- 9.M.C. Golumbic and U. Rotics. On the clique-width of perfect graph classes. In Proceedings of Graph-Theoretical Concepts in Computer Science, volume 1665 of LNCS, pages 135–147. Springer-Verlag, 1999.Google Scholar
- 10.F. Gurski. Algorithmische Charakterisierungen spezieller Graphklassen. Diplomarbeit, Heinrich-Heine-Universität, Düsseldorf, Germany, 1998.Google Scholar
- 11.Ö. Johansson. Clique-decomposition, NLC-decomposition, and modular decomposition-relationships and results for random graphs. Congressus Numerantium, 132:39–60, 1998.Google Scholar
- 12.Ö. Johansson. NLC2 decomposition in polynomial time. In Proceedings of GraphTheoretical Concepts in Computer Science, volume 1665 of LNCS, pages 110–121.Springer-Verlag, 1999.Google Scholar