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A simplex like approach based on star sets for recognizing convex- $$QP$$ Q P adverse graphs

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  • Domingos M. Cardoso

    (University of Aveiro)

  • Carlos J. Luz

    (University of Aveiro)

Abstract

A graph $$G$$ G with convex- $$QP$$ Q P stability number (or simply a convex- $$QP$$ Q P graph) is a graph for which the stability number is equal to the optimal value of a convex quadratic program, say $$P(G)$$ P ( G ) . There are polynomial-time procedures to recognize convex- $$QP$$ Q P graphs, except when the graph $$G$$ G is adverse or contains an adverse subgraph (that is, a non complete graph, without isolated vertices, such that the least eigenvalue of its adjacency matrix and the optimal value of $$P(G)$$ P ( G ) are both integer and none of them changes when the neighborhood of any vertex of $$G$$ G is deleted). In this paper, from a characterization of convex- $$QP$$ Q P graphs based on star sets associated to the least eigenvalue of its adjacency matrix, a simplex-like algorithm for the recognition of convex- $$QP$$ Q P adverse graphs is introduced.

Suggested Citation

  • Domingos M. Cardoso & Carlos J. Luz, 2016. "A simplex like approach based on star sets for recognizing convex- $$QP$$ Q P adverse graphs," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 311-326, January.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:1:d:10.1007_s10878-014-9745-x
    DOI: 10.1007/s10878-014-9745-x
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    References listed on IDEAS

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    1. Carlos Luz & Domingos Cardoso, 1998. "A generalization of the Hoffman - Lovász upper boundon the independence number of a regular graph," Annals of Operations Research, Springer, vol. 81(0), pages 307-320, June.
    2. Carlos Luz, 2005. "Improving an Upper Bound on the Stability Number of a Graph," Journal of Global Optimization, Springer, vol. 31(1), pages 61-84, January.
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