The Sandwich Theorem

This report contains expository notes about a function $\theta(G)$ that is popularly known as the Lovász number of a graph $G$. There are many ways to define $\theta(G)$, and the surprising variety of different characterizations indicates in itself that $\theta(G)$ should be interesting. But the most interesting property of $\theta(G)$ is probably the fact that it can be computed efficiently, although it lies "sandwiched" between other classic graph numbers whose computation is NP-hard. I have tried to make these notes self-contained so that they might serve as an elementary introduction to the growing literature on Lovász's fascinating function. This report contains expository notes about a function $\theta(G)$ that is popularly known as the Lovász number of a graph $G$. There are many ways to define $\theta(G)$, and the surprising variety of different characterizations indicates in itself that $\theta(G)$ should be interesting. But the most interesting property of $\theta(G)$ is probably the fact that it can be computed efficiently, although it lies "sandwiched" between other classic graph numbers whose computation is NP-hard. I have tried to make these notes self-contained so that they might serve as an elementary introduction to the growing literature on Lovász's fascinating function.