On the Complexity of the Independent Set Problem in Triangle Graphs
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Discrete Mathematics 311 (2011) 1670–1680 Contents lists available at ScienceDirect Discrete Mathematics journal homepage: www.elsevier.com/locate/disc On the complexity of the independent set problem in triangle graphs Yury Orlovich a,∗, Jacek Blazewicz b, Alexandre Dolgui c, Gerd Finke d, Valery Gordon e a Department of Discrete Mathematics and Algorithmics, Faculty of Applied Mathematics and Computer Science, Belarusian State University, Nezavisimosti Ave. 4, 220030 Minsk, Belarus b Institute of Computing Science, Poznan University of Technology, ul. Piotrowo 3a, Poznan, Poland c Ecole Nationale Supérieure des Mines de Saint-Etienne, Centre for Industrial Engineering and Computer Science, 158 cours Fauriel, F-42023 Saint Etienne Cedex 2, France d Laboratoire G-SCOP, Université Joseph Fourier, 46 Avenue Félix Viallet, 38031 Grenoble Cedex, France e United Institute of Informatics Problems, National Academy of Sciences of Belarus, 6 Surganova Str., 220012 Minsk, Belarus article info a b s t r a c t Article history: We consider the complexity of the maximum (maximum weight) independent set problem Received 29 October 2009 within triangle graphs, i.e., graphs G satisfying the following triangle condition: for every Received in revised form 31 March 2011 maximal independent set I in G and every edge uv in G − I, there is a vertex w 2 I Accepted 2 April 2011 such that fu; v; wg is a triangle in G. We also introduce a new graph parameter (the Available online 27 April 2011 upper independent neighborhood number) and the corresponding upper independent neighborhood set problem.
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