From tree-decompositions to clique-width terms

Bruno Courcelle (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

Tree-width and clique-width are two important graph complexity measures that serve as parameters in many fixed-parameter tractable algorithms. We give two algorithms that transform tree-decompositions represented by normal trees into clique-width terms. As a consequence, we obtain that for sparse graphs, clique-width is polynomially bounded in terms of tree-width. It is even linearly bounded for planar graphs and incidence graphs. These results have applications to model-checking algorithms for problems described by monadic second-order formulas, including those allowing edge set quantifications.

Mots clés: tree-width; clique-width; planar graph; sparse graph

Domaines: Logique en informatique [cs.LO]

Bruno Courcelle. From tree-decompositions to clique-width terms. Discrete Applied Mathematics, 2018. ⟨hal-01398972⟩