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 
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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[1] A. Brandstädt, V.B. Le and J.P. Spinrad, Graph Classes: A Survey (Society for Industrial and Applied Mathematics, Philadelphia, 1999). doi:10.1137/1.9780898719796

[2] R.C.S. Machado, C.M.H. de Figueiredo and N. Trotignon, Complexity of colouring problems restricted to unichord-free and { square, unichord }- free graphs, Discrete Appl. Math. 164 (2014) 191–199. doi:10.1016/j.dam.2012.02.016

[3] R.C.S. Machado, C.M.H. de Figueiredo and K. Vušković, Chromatic index of graphs with no cycle with a unique chord, Theoret. Comput. Sci. 411 (2010) 1221–1234. doi:10.1016/j.tcs.2009.12.018

[4] T.A. McKee, Independent separator graphs, Util. Math. 73 (2007) 217–224.

[5] T.A. McKee, Minimal vertex separators and 3- skein subgraphs, Bull. Inst. Combin. Appl. 72 (2014) 19–24.

[6] T.A. McKee, A new characterization of unichord-free graphs, Discuss. Math. Graph Theory 35 (2015) 765–771. doi:10.7151/dmgt.1831

[7] T.A. McKee and F.R. McMorris, Topics in Intersection Graph Theory (Society for Industrial and Applied Mathematics, Philadelphia, 1999). doi:10.1137/1.9780898719802

[8] N. Trotignon and K. Vušković, A structure theorem for graphs with no cycle with a unique chord and its consequences, J. Graph Theory 63 (2010) 31–67. doi:10.1002/jgt.20405