# Exactness of Parrilo's conic approximations for copositive matrices and associated low order bounds for the stability number of a graph

@inproceedings{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}, year={2021} }

De Klerk and Pasechnik (2002) introduced the bounds θ(G) (r ∈ N) for the stability number α(G) of a graph G and conjectured exactness at order α(G) − 1: θ(G) = α(G). These bounds rely on the conic approximations K (r) n by Parrilo (2000) for the copositive cone COPn. A difficulty in the convergence analysis of θ is the bad behaviour of the cones K (r) n under adding a zero row/column: when applied to a matrix not in K (0) n this gives a matrix not in any K (r) n+1, thereby showing strict…

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