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Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones....
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 ...
We show that Edge Dominating Set, Hamiltonian Cycle, and Graph Coloring are W[1]-hard parameterized by clique-width. It was an open problem, explicitly mentioned in several papers,...
Fedor V. Fomin, Petr A. Golovach, Daniel Lokshtano...
Clique-width is an important graph parameter whose computation is NP-hard. In fact we do not know of any other algorithm than brute force for the exact computation of clique-width...
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, ...