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...ghout our paper to other combinatorial problems such as decomposition into “inheritance-block” of an inheritance graph in O(n + m) time, which would yield an alternative to the algorithms proposed in =-=[6,16]-=-. Another example would be the modular decomposition in O(n) time of a bounded tolerance graph – trapezoid graph with solely parallelograms [5,13] – when an intersection model is provided. Then, it wo...

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... [14]. Our algorithm can be seen as a common generalization of Hsu and Ma [16, 15] for modular decomposition of chordal graphs and Habib, Huchard and Spinrad [10] for inheritance graphs decomposition =-=[1]-=-. It also suggests many new decomposition algorithms for various notions of graph decompositions. Keywords: Graph algorithms, graph decompositions, modular decomposition. 1 General decomposition frame...

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...of rank k (see [20]). In both cases the families of sets are MS definable and Proposition 2.2 is applicable. 2.3. Factors in directed acyclic graphs. We review some results of Courcelle [11], Capelle =-=[3]-=-, Habib et al. [23] concerning directed acyclic graphs. We show that they can be reformulated in the framework of this section and slightly improved. Definition 2.9. 2-graphs and 2-dags In this subsec...

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...o elements a and b which represent ∨-irreducible elements and ∧-irreducible elements of the bimodule. This last case is a particular case of another decomposition proposed for inheritance hierarchies =-=[2]-=-, called the block decomposition (with a different definition of block that the one in [5]): a block is an interval [a, b] such that only a and b can be distinguished of other vertices from the outsid...