The graphs in which every minimal vertex separator induces a complete or an edgeless subgraph are shown to be the edge sums of graphs of the two extreme types: (i) when every minimal vertex separator induces a complete subgraph — these are precisely the well-studied chordal graphs — and (ii) when every minimal vertex separator induces an edgeless subgraph — these have appeared in several recent papers.
['Terry A. McKee']
WHEN ALL MINIMAL VERTEX SEPARATORS INDUCE COMPLETE OR EDGELESS SUBGRAPHS