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

Noga Alon, Eyal Lubetzky

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

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 subpolynomial 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.

Original languageEnglish (US)
Pages (from-to)2172-2176
Number of pages5
JournalIEEE Transactions on Information Theory
Volume52
Issue number5
DOIs
StatePublished - May 2006

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Keywords

  • Graph powers
  • Shannon capacity

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