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

arXiv eprints
 Pub Date:
 August 2006
 arXiv:
 arXiv:cs/0608021
 Bibcode:
 2006cs........8021A
 Keywords:

 Computer Science  Information Theory;
 Computer Science  Discrete Mathematics
 EPrint:
 IEEE Trans. on Information Theory 52 (2006), 21722176