Separability generalizes Dirac's theorem (1998)
by
Anne Berry
,
Jean-paul Bordat
| Citations: | 15 - 10 self |
BibTeX
@MISC{Berry98separabilitygeneralizes,
author = {Anne Berry and Jean-paul Bordat},
title = {Separability generalizes Dirac's theorem},
year = {1998}
}
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Abstract
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.
