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The sandwich theorem

Donald E. Knuth
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Abstract

This report contains expository notes about a function $\vartheta(G)$ that is popularly known as the Lovász 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 Lovász's fascinating function.

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Donald E. Knuth. 1993-12-06. The sandwich theorem. https://arxiv.org/abs/math/9312214

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