Geodesic
Requiring that Minimal Separators Induce Complete Multipartite Subgraphs
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 263-273.

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Complete multipartite graphs range from complete graphs (with every partite set a singleton) to edgeless graphs (with a unique partite set). Requiring minimal separators to all induce one or the other of these extremes characterizes, respectively, the classical chordal graphs and the emergent unichord-free graphs. New theorems characterize several subclasses of the graphs whose minimal separators induce complete multipartite subgraphs, in particular the graphs that are 2-clique sums of complete, cycle, wheel, and octahedron graphs.
Keywords: minimal separator, complete multipartite graph, chordal graph, unichord-free graph 
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McKee, Terry A. Requiring that Minimal Separators Induce Complete Multipartite Subgraphs. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 263-273. http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a20/

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