On the Lovasz O-Number of Almost Regular Graphs with Application to Erdos-Renyi Graphs

Center Discussion Paper Series No. 2006-93

12 Pages Posted: 12 Oct 2006

See all articles by Etienne de Klerk

Etienne de Klerk

Tilburg University

M. Newman

Queen Mary, University of London

Dmitrii V. Pasechnik

Tilburg University - Center for Economic Research (CentER)

Renata Sotirov

Tilburg University - Tilburg University School of Economics and Management

Date Written: September 2006

Abstract

We consider k-regular graphs with loops, and study the Lovasz O-numbers and Schrijver O-numbers of the graphs that result when the loop edges are removed. We show that the O-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. Journal of Combinatorial Theory B, to appear]. As an application we compute the O and O numbers of certain instances of Erdos Renyi 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. Mathematical Programming B, to appear]. The computed values are strictly better than the Godsil-Newman eigenvalue bounds.

Keywords: Erdos-Renyi graph, stability number, Lovasz O-number, Schrijver O-number, C*-algebra, semidefinite programming

JEL Classification: C60

Suggested Citation

de Klerk, Etienne and Newman, M. and Pasechnik, Dmitrii V. and Sotirov, Renata, On the Lovasz O-Number of Almost Regular Graphs with Application to Erdos-Renyi Graphs (September 2006). Available at SSRN: https://ssrn.com/abstract=936910 or http://dx.doi.org/10.2139/ssrn.936910

Etienne De Klerk (Contact Author)

Tilburg University ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

M. Newman

Queen Mary, University of London ( email )

Mile End Road
London, London E1 4NS
United Kingdom

Dmitrii V. Pasechnik

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Renata Sotirov

Tilburg University - Tilburg University School of Economics and Management ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

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