TITLE: What is the maximum of the ratio $\vartheta(G)/\alpha(G)$?
QUESTION [6 upvotes]: A maximum independent set is a largest independent set for a given graph $G$ and its size is denoted $\alpha(G)$. And the Lovász number of $G$ is denoted $\vartheta(G)$. $\vartheta(G)\geq \alpha(G)$ by definition, then the question is what will the 
$$\max\limits_G \frac{\vartheta(G)}{\alpha(G)}$$
be? Any known results about this topic will be welcome! One can give examples to show how big could the ratio $\vartheta(G)/\alpha(G)$ be or counter-examples to show the ratio will go to infinity. Any help or suggestions will be appreciated!
P.S. here is a related question:Cliques, Paley graphs and quadratic residues.

REPLY [6 votes]: It is infinite, in fact much stronger versions are also true, see e.g., Theorem 1 here:
http://arxiv.org/abs/cs/0608021
(Shannon capacity is between $\alpha$ and $\vartheta$.)