2006/08/03 by Noga Alon, Eyal Lubetzky · 1 citation
Computer Science · Mathematics · #cs.DM #cs.IT #math.IT
paper · pdf · doi:10.1109/tit.2006.872856
published as IEEE Trans. on Information Theory 52 (2006), 2172-2176
arxiv created 2006/08/03 · arxiv updated 2016/11/17
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.