Paper Info
Title
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.
Year
DOI
Venue
2006
10.1109/TIT.2006.872856
IEEE Transactions on Information Theory
Keywords
DocType
Volume
complex structure,fixed graph,strong power,subpolynomial factor,shannon capacity,graph product,independence number,significant increase,strong graph product,hilbert space,channel capacity,graph theory,upper bound,pareto analysis,feedback,polynomial factorization,information theory,graph power,reliability theory
Journal
52
Issue
ISSN
Citations 
5
IEEE Trans. on Information Theory 52 (2006), 2172-2176
10
PageRank 
References 
Authors
0.70
8
2
Name
Order
Citations
PageRank
Noga Alon1104681688.16
Eyal Lubetzky235528.87