Gap, cosum, and product properties of the $\theta’$ bound on the clique number

In a paper published 1978, McEliece, Rodemich and Rumsey improved Lov\'asz' bound for the Maximum Clique Problem. This strengthening has become well-known under the name Lov\'asz-Schrijver bound and is usually denoted by $\theta'$. This article now deals with situations where this bound is not exact. To provide instances for which the gap between this bound and the actual clique number can be arbitrarily large, we establish homomorphy results for this bound under cosums and products of graphs, and study the special class of circulant graphs: here we show that for circulant graphs of prime order there must be a positive gap between the clique number and the bound.


Technical Report TR-ISDS {\bf 2007-06}, University of Vienna, to appear in: Optimization (2010).



View Gap, cosum, and product properties of the $ heta'$ bound on the clique number