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Graph Structure and Monadic Second-Order Logic by Joost Engelfriet, Bruno Courcelle

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2.4.4 Tree-decompositions and chordal graphs

We consider the graphs that have tree-decompositions, all boxes of which induce cliques. Efficient algorithms for chordal graphs, based on their tree-decompositions, are presented in [Gav] and [*Gol].

Definition 2.71 (Chordal graphs) Let be the class of nonempty, connected, simple and loop-free undirected graphs. Let k+. A graph G in is k-chordal if it has a tree-decomposition, each box of which is ...

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