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CORR
2006
Springer

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

9 years 11 months ago
The Shannon capacity of a graph and the independence numbers of its powers
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 sub-polynomial factor of the number of vertices) by any arbitrarily large, yet fixed, prefix of the series. This is true even if this prefix shows a significant increase of the independence number at a given power, after which it stabilizes for a while.
Noga Alon, Eyal Lubetzky
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where CORR
Authors Noga Alon, Eyal Lubetzky
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