# Approximation of the Stability Number of a Graph via Copositive Programming

@article{Klerk2002ApproximationOT, title={Approximation of the Stability Number of a Graph via Copositive Programming}, author={Etienne de Klerk and Dmitrii V. Pasechnik}, journal={SIAM J. Optim.}, year={2002}, volume={12}, pages={875-892} }

Lovasz and Schrijver [SIAM J. Optim., 1 (1991), pp. 166--190] showed how to formulate increasingly tight approximations of the stable set polytope of a graph by solving semidefinite programs (SDPs) of increasing size (lift-and-project method). In this paper we present a similar idea. We show how the stability number can be computed as the solution of a conic linear program (LP) over the cone of copositive matrices. Subsequently, we show how to approximate the copositive cone ever more closely…

## 336 Citations

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This work is based on and refines de Klerk and Pasechnik’s approach to approximating the stability number via copositive programming and provides a closed-form expression for the values computed by the linear programming approximations.

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