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    Rights statement: This is the author’s version of a work that was accepted for publication in Discrete Optimization. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Optimization, 25, 2017 DOI: 10.1016/d.disopt.2017.04.001

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On the Lovász theta function and some variants

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>27/07/2017
<mark>Journal</mark>Discrete Optimization
Volume25
Number of pages16
Pages (from-to)159-174
Publication statusPublished
Early online date13/05/17
Original languageEnglish

Abstract

The Lovász theta function of a graph is a well-known upper bound on the stability number. It can be computed efficiently by solving a semidefinite program (SDP). Actually, one can solve either of two SDPs, one due to Lovász and the other to Grötschel et al. The former SDP is often thought to be preferable computationally, since it has fewer variables and constraints. We derive some new results on these two equivalent SDPs. The surprising result is that, if we weaken the SDPs by aggregating constraints, or strengthen them by adding cutting planes, the equivalence breaks down. In particular, the Grötschel et al. scheme typically yields a stronger bound than the Lovász one.

Bibliographic note

This is the author’s version of a work that was accepted for publication in Discrete Optimization. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Optimization, 25, 2017 DOI: 10.1016/d.disopt.2017.04.001