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On the complexity of the independent set problem in triangle graphs

Abstract : We consider the complexity of the maximum independent set problem within triangle graphs, i.e., graphs G satisfying the following triangle condition: for every maximal independent set I in G and every edge uv in G¡I, there is a vertex w 2 I such that fu; v;wg is a triangle in G. We also introduce a new graph parameter (upper independent neighborhood number) and the corresponding upper independent neighborhood set problem. We show that for triangle graphs the new parameter equals to the independence number. Finally, we prove that the problems under consideration are NP-complete for triangle graphs and provide some polynomially solvable cases for these problems within triangle graphs.
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Contributor : Florent Breuil Connect in order to contact the contributor
Submitted on : Friday, March 16, 2012 - 1:30:36 PM
Last modification on : Wednesday, August 4, 2021 - 3:42:04 PM


  • HAL Id : emse-00679806, version 1


Jacek Blazewicz, Alexandre Dolgui, Valery Gordon, Yury Orlovich. On the complexity of the independent set problem in triangle graphs. 2009. ⟨emse-00679806⟩



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