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Modular decomposition and transitive orientation. (English) Zbl 0933.05146
A module of a graph $$G$$ is a set $$X$$ of vertices such that, for every $$x\in V(G)-X$$, either $$x$$ is adjacent to every element of $$X$$ or $$x$$ is adjacent to no vertex in $$X$$. The modular decomposition of $$G$$ is an $$O(n)$$-space representation of the modules of $$G$$. The authors introduce linear time algorithms to construct the modular decomposition of a graph and a transitive orientation of a comparability graph. Note that a linear time algorithm for the modular decompositions of both directed and undirected graphs was suggested by A. Cournier and M. Habib [Lect. Notes Comput. Sci. 657, 212-224 (1993)].
Reviewer: G.Gutin (Odense)

##### MSC:
 05C85 Graph algorithms (graph-theoretic aspects) 05C05 Trees
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