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A limit theorem for the Shannon capacities of odd cycles. II
Authors:Tom Bohman
Affiliation:Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Abstract:It follows from a construction for independent sets in the powers of odd cycles given in the predecessor of this paper that the limit as $k$ goes to infinity of $ k + 1/2 - Theta( C_{2k+1} ) $ is zero, where $ Theta(G) $is the Shannon capacity of a graph $G$. This paper contains a shorter proof of this limit theorem that is based on an `expansion process' introduced in an older paper of L. Baumert, R. McEliece, E. Rodemich, H. Rumsey, R. Stanley and H. Taylor. We also refute a conjecture from that paper, using ideas from the predecessor of this paper.

Keywords:Shannon capacity   odd cycles
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