# The Shannon capacity of a graph and the independence numbers of its powers

@article{Alon2006TheSC, title={The Shannon capacity of a graph and the independence numbers of its powers}, author={Noga Alon and Eyal Lubetzky}, journal={IEEE Transactions on Information Theory}, year={2006}, volume={52}, pages={2172-2176} }

The independence numbers of powers of graphs have been long studied, under several definitions of graph products, and in particular, under the strong graph product. We show that the series of independence numbers in strong powers of a fixed graph can exhibit a complex structure, implying that the Shannon capacity of a graph cannot be approximated (up to a subpolynomial factor of the number of vertices) by any arbitrarily large, yet fixed, prefix of the series. This is true even if this prefix…

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