The sandwich theorem
Summary: 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.
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