# Discrete Mathematics & Theoretical Computer Science

## Volume 4 n° 1 (2000), pp. 45-60

author: | Ross M. McConnell and Jeremy P. Spinrad |
---|---|

title: | Ordered Vertex Partitioning |

keywords: | Modular Decomposition, Substitution Decomposition, Transitive Orientation |

abstract: | A transitive orientation of a graph is an orientation of the edges that produces a transitive digraph. The modular decomposition
of a graph is a canonical representation of all of its modules.
Finding a transitive orientation and finding the modular decomposition
are in some sense dual problems.
In this paper, we describe a simple O(n + m log n) algorithm that
uses this duality to find both a transitive orientation and the
modular decomposition.
Though the running time is not optimal, this algorithm
is much simpler than any previous algorithms that are not Ω(n.
The best known time bounds for the problems are ^{2})O(n+m) but they
involve sophisticated techniques.
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reference: | Ross M. McConnell and Jeremy P. Spinrad (2000),
Ordered Vertex Partitioning,
Discrete Mathematics and Theoretical Computer Science 4, pp. 45-60 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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