Geodesic
A New Characterization of Unichord-Free Graphs
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 4, pp. 765-771

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Unichord-free graphs are defined as having no cycle with a unique chord. They have appeared in several papers recently and are also characterized by minimal separators always inducing edgeless subgraphs (in contrast to characterizing chordal graphs by minimal separators always inducing complete subgraphs). A new characterization of unichord-free graphs corresponds to a suitable reformulation of the standard simplicial vertex characterization of chordal graphs.
Keywords: chordal graph, unichord-free graph, minimal separator 
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McKee, Terry A. A New Characterization of Unichord-Free Graphs. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 4, pp. 765-771. http://geodesic.mathdoc.fr/item/DMGT_2015_35_4_a12/