This paper shows how the stability number can be computed as the solution of a conic linear program (LP) over the cone of copositive matrices of a graph by solving semidefinite programs (SDPs) of increasing size (lift-and-project method).Expand

A general technique to reduce the size ofSemidefinite programming problems on which a permutation group is acting is described, based on a low-order matrix based on the representation of the commutant (centralizer ring) of the matrix algebra generated by the permutation matrices.Expand

This work constructs polynomial-size bounded degree LSd proofs of the clique-coloring tautologies, the symmetric knapsack problem, and Tseitin's tautology, and proves lower bounds on Lovasz-Schrijver ranks, demonstrating, in particular, their rather limited applicability for proof complexity.Expand

A detailed algorithmic study of the cost of stability in weighted voting games, a simple but expressive class of games which can model decision-making in political bodies, and cooperation in multiagent settings is provided.Expand

Improved bounds on the asymptotic ratios of these crossing numbers and their conjectured values are shown, obtained as a consequence of the new bound on $\Cr(\ksn) 2.1796n^2 - 4.5n".Expand

This paper shows that the approximation to the chromatic number suggested in De Klerk et al. (2000) is bounded from above by the Lovász θ-function, and suggests a provably good MAX-k-CUT algorithm, and shows that of the algorithm is closely related to that of Frieze and Jerrum.Expand

A procedure that computes, in (dn)O(k) arithmetic operations in D, a set of sampling points in D that intersects nontrivially each connected component of Z that is polynomial-time for constant k.Expand