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

Authors
  • Alon, Noga
  • Lubetzky, Eyal
Type
Published Article
Publication Date
Aug 03, 2006
Submission Date
Aug 03, 2006
Identifiers
arXiv ID: cs/0608021
Source
arXiv
License
Unknown
External links

Abstract

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.

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