Tree-width and clique-width are two important graph complexity measures that serve as parameters in many fixed-parameter tractable (FPT) algorithms. The same classes of sparse graphs, in particular of planar graphs and of graphs of bounded degree have bounded tree-width and bounded clique-width. We prove that, for sparse graphs, clique-width is polynomially bounded in terms of tree-width. For p...

We show that there exists a linear time algorithm for deciding whether a graph of bounded tree-width has clique-width k for some fixed integer k. Communicated by Giuseppe Liotta and Ioannis G. Tollis: submitted October 2001; revised July 2002 and February 2003. The work of the second author was supported by the German Research Association (DFG) grant WA 674/9-2. W. Espelage et al., Deciding Cli...

PETR HLINĚNÝ1,2,*, SANG-IL OUM3,7, DETLEF SEESE4 AND GEORG GOTTLOB5,6 Faculty of Informatics, Masaryk University, Botanická 68a, 602 00 Brno, Czech Republic VŠB, Technical University of Ostrava, Ostrava, Czech Republic School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA Institute AIFB, University Karlsruhe (TH), D-76128 Karlsruhe, Germany Oxford University Comput...

We give a simple proof that the straightforward generalisation of clique-width to arbitrary structures can be unbounded on structures of bounded tree-width. This can be corrected by allowing fusion of elements.

We show that for every forest T the linear rank-width of T is equal to the path-width of T , and the linear clique-width of T equals the path-width of T plus two, provided that T contains a path of length three. It follows that both linear rank-width and linear clique-width of forests can be computed in linear time. Using our characterization of linear rank-width of forests, we determine the se...

The width of a subset C of the vertices of a distance-regular graph is the maximum distance which occurs between elements of C. Dually, the dual width of a subset in a cometric association scheme is the index of the “last” eigenspace in the Q-polynomial ordering to which the characteristic vector of C is not orthogonal. Elementary bounds are derived on these two new parameters. We show that any...