On simplicial and co-simplicial vertices in graphs

Authors:
Chınh T Hoíng;Stefan Hougardy;Frédéric Maffray;N. V. R Mahadev
Affiliations:
Department of Physics and Computer Science, Wilfrid Laurier University, 75 University Ave. W., Waterloo, Ont., Canada N2L 3C5;Institut für Informatik, Humboldt-Universität zu Berlin Unter den Linden 6, Berlin 10099, Germany;C.N.R.S., Laboratoire Leibniz-IMAG, 46 Avenue Félix Viallet, Grenoble Cedex 38031, France;Department of Computer Science, Fitchburg State College, Fitchburg, MA 01420, USA
Venue:
Discrete Applied Mathematics
Year:
2004

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Abstract

We investigate the class of graphs defined by the property that every induced subgraph has a vertex which is either simplicial (its neighbours form a clique) or co-simplicial (its non-neighbours form an independent set). In particular we give the list of minimal forbidden subgraphs for the subclass of graphs whose vertex-set can be emptied out by first recursively eliminating simplicial vertices and then recursively eliminating co-simplicial vertices.