Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/94538
Title: On the Lovász ϑ-number of almost regular graphs with application to Erdős–Rényi graphs
Authors: Sotirov, R.
Klerk, Etienne de.
Newman, M. W.
Pasechnik, Dmitrii V.
Keywords: DRNTU::Science::Mathematics
Issue Date: 2008
Source: Klerk, E. D., Newman, M. W., Pasechnik, D. V. & Sotirov R. (2009). On the Lovász ϑ-number of almost regular graphs with application to Erdős–Rényi graphs. European Journal of Combinatorics, 30(4), 879–888
Series/Report no.: European journal of combinatorics
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.
URI: https://hdl.handle.net/10356/94538
http://hdl.handle.net/10220/7516
DOI: 10.1016/j.ejc.2008.07.022
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 ]
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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