- | ||||
|
![]()
|
On the Lovász theta-number of almost regular graphs with application to Erdös--Rényi graphs
Etienne De Klerk (e.deklerk Abstract: We consider k-regular graphs with loops, and study the Lovász theta-numbers and Schrijver theta'-numbers of the graphs that result when the loop edges are removed. We show that the theta-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 theta and theta'-numbers of certain instances of Erdös--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.Mathematical Programming B, to appear]. The computed values are strictly better than the Godsil-Newman eigenvalue bounds. Keywords: Erdos-Renyi graph, stability number, Lovasz theta-number, Schrijver theta'-number, semidefinite programming Category 1: Combinatorial Optimization (Graphs and Matroids ) Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming ) Citation: CentER Discussion Paper 2006-93 Tilburg University The Netherlands Download: [PDF] Entry Submitted: 09/28/2006 Modify/Update this entry | ||
Visitors | Authors | More about us | Links | |
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository
|
Submit Update Policies |
Coordinator's Board Classification Scheme Credits Give us feedback |
Optimization Journals, Sites, Societies | |
![]() |