We investigate hierarchies of semidefinite approximations for the chromatic number $\chi(G)$ of a graph $G$, improving the classic Lovasz theta number (and its strengthenings obtained by adding nonnegativity and triangle inequalities); experimental results are given in the follow-up paper.Expand

Lovász and Schrijver (SIAM J. Optim. 1:166–190, 1991) have constructed semidefinite relaxations for the stable set polytope of a graph G = (V,E) by a sequence of lift-and-project operations.Expand

We propose two new, block-diagonal hierarchies of semidefinite programming relaxations, which are at least as strong as the Lovasz-Schrijver hierarchy, but less costly to compute.Expand

Because of increasing interest in cryptocurrency investments, there is a need to quantify their variation over time. Therefore, in this paper we try to answer a few important questions related to a… Expand

We construct a hierarchy of semidefinite relaxations for the stable set polytope of a graph G = (V,E) by a sequence of lift-and-project operations, where α(G) is the stability number of G.Expand

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This paper extends the existing GQM + Strategies knowledge base by further elaborating and clarifying the process of creating grids by introducing causality theory.Expand