an:06937768
Zbl 1395.05097
Courcelle, Bruno
From tree-decompositions to clique-width terms
EN
Discrete Appl. Math. 248, 125-144 (2018).
00414462
2018
j
05C42 05C10 05C12 05C85
tree-width; clique-width; sparse graph; planar graph; incidence graph; fixed-parameter tractable algorithm
Summary: 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 (a rooted tree is normal for a graph if its nodes are the vertices of the graph and every two adjacent vertices are on a path of the tree starting at the root). As a consequence, we obtain that, for certain classes of 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 are useful in the construction of model-checking algorithms for problems described by monadic second-order formulae, including those allowing edge set quantifications.