# Exactness of Parrilo’s Conic Approximations for Copositive Matrices and Associated Low Order Bounds for the Stability Number of a Graph

@article{Laurent2021ExactnessOP,
title={Exactness of Parrilo’s Conic Approximations for Copositive Matrices and Associated Low Order Bounds for the Stability Number of a Graph},
author={Monique Laurent and Luis Felipe Vargas},
journal={Mathematics of Operations Research},
year={2021}
}
• Published 27 September 2021
• Mathematics
• Mathematics of Operations Research
De Klerk and Pasechnik introduced in 2002 semidefinite bounds [Formula: see text] for the stability number [Formula: see text] of a graph G and conjectured their exactness at order [Formula: see text]. These bounds rely on the conic approximations [Formula: see text] introduced by Parrilo in 2000 for the copositive cone [Formula: see text]. A difficulty in the convergence analysis of the bounds is the bad behavior of Parrilo’s cones under adding a zero row/column: when applied to a matrix not…

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