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DAM

1998

1998

In our study of the extremities of a graph, we deﬁne a moplex as a maximal clique module the neighborhood of which is a minimal separator of the graph. This notion enables us to strengthen Dirac’s theorem (Dirac, 1961): ‘‘Every non-clique triangulated graph has at least two non-adjacent simplicial vertices’’, restricting the deﬁnition of a simplicial vertex; this also enables us to strengthen Fulkerson and Gross’ simplicial elimination scheme; thus provides a new characterization for triangulated graphs. Our version of Dirac’s theorem generalizes from the class of triangulated graphs to any undirected graph: ‘‘Every non-clique graph has at least two non-adjacent moplexes’’. To insure a linear-time access to a moplex in any graph, we use an algorithm due to Rose Tarjan and Lueker (1976) for the recognition of triangulated graphs, known as LexBFS: we prove a new invariant for this, true even on non-triangulated graphs. 1998 Elsevier Science B.V. All rights rese...

Related Content

Added |
22 Dec 2010 |

Updated |
22 Dec 2010 |

Type |
Journal |

Year |
1998 |

Where |
DAM |

Authors |
Anne Berry, Jean Paul Bordat |

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