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On the Lovász ϑ-number of almost regular graphs with application to Erdős–Rényi graphs.

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On the Lovász ϑ-number of almost regular graphs with application to Erdős–Rényi graphs.

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Title: On the Lovász ϑ-number of almost regular graphs with application to Erdős–Rényi graphs.
Author: Klerk, Etienne de.; Newman, M. W.; Pasechnik, Dmitrii V.; Sotirov, R.
Copyright year: 2008
Abstract: We consider k-regular graphs with loops, and study the Lovász ϑ-numbers and Schrijver ϑ′-numbers of the graphs that result when the loop edges are removed. We show that the ϑ-number dominates a recent eigenvalue upper bound on the stability number due to Godsil and Newman [C.D. Godsil and M.W. Newman. Eigenvalue bounds for independent sets, J. Combin. Theory B 98 (4) (2008) 721–734]. As an application we compute the ϑ and ϑ′ numbers of certain instances of Erdős–Rényi graphs. This computation exploits the graph symmetry using the methodology introduced in [E. de Klerk, D.V. Pasechnik and A. Schrijver, Reduction of symmetric semidefinite programs using the regular *-representation, Math. Program. B 109 (2–3) (2007) 613–624]. The computed values are strictly better than the Godsil–Newman eigenvalue bounds.
Subject: DRNTU::Science::Mathematics.
Type: Journal Article
Series/ Journal Title: European journal of combinatorics
School: School of Physical and Mathematical Sciences
Rights: © 2008 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by European Journal of Combinatorics, Elsevier.  It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document.  The published version is available at: [DOI: http://dx.doi.org/10.1016/j.ejc.2008.07.022 ]
Version: Accepted version

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