A limit theorem for the Shannon capacities of odd cycles. II

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.