New decompositions of 2-structures
Résumé
We present a family of decompositions of $2$-structures generalizing the modular decomposition, and $O(n^3)$ time algorithms to compute all these decompositions. These results can be applied to non-oriented, oriented and directed graphs. Bi-join decomposition of non-oriented graphs and of tournaments are two special cases of this family of decomposition. Two others special cases are generalizations of the bi-join decomposition on directed graphs.
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