Stable-Set and Coloring bounds based on 0-1 quadratic optimization

TL;DR

This paper introduces new semidefinite relaxations for Stable-Set and Coloring problems based on quadratic 0-1 optimization, utilizing graph properties to simplify and tighten bounds, with promising computational results.

Contribution

It proposes novel relaxations and tightenings for Stable-Set and Coloring based on quadratic 0-1 optimization, improving bounds using graph structure.

Findings

Relaxations depend mainly on the number of vertices.

Tightenings based on maximal cliques improve bounds.

Computational results show strong potential of the approach.

Abstract

We consider semidefinite relaxations of Stable-Set and Coloring, which are based on quadratic 0-1 optimization. Information about the stability number and the chromatic number is hidden in the objective function. This leads to simplified relaxations which depend mostly on the number of vertices of the graph. We also propose tightenings of the relaxations which are based on the maximal cliques of the underlying graph. Computational results on graphs from the literature show the strong potential of this new approach.