Cybernetics and Systems Analysis

, Volume 45, Issue 1, pp 141–152 | Cite as

LP-oriented upper bounds for the weighted stability number of a graph

  • P. I. StetsyukEmail author
  • A. P. Lykhovyd
Systems Analysis

Upper bounds for the weighted stability number of a graph are considered that are based on the approximation of its stable set polytope by linear inequalities for odd cycles and p-wheels in the graph. Algorithms are developed for finding upper bounds on the basis of solution of LP problems with a finite number of inequalities produced by the shortest path algorithm for a special graph. The results of test experiments are given for graphs with several hundred or thousand vertices.


weighted stability number of a graph polyhedron of stable sets LP-oriented upper bound t-perfect graph p-wheel Wp-perfect graph 


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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Cybernetics InstituteNational Academy of Sciences of UkraineKievUkraine

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