The Sandwich Theorem

This report contains expository notes about a function vartheta(G) that is popularly known as the Lovasz number of a graph G. There are many ways to define vartheta(G), and the surprising variety of different characterizations indicates in itself that vartheta(G) should be interesting. But the most interesting property of vartheta(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 Lovasz''s fascinating function.

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