The Shannon capacity of a union

For an undirected graph G = (V, E), let G n denote the graph whose vertex set is V n in which two distinct vertices (u1, u2,..., un) and (v1, v2,..., vn) are adjacent iff for all i between 1 and n either ui = vi or uivi ∈ E. The Shannon capacity c(G) of G is the limit limn→∞(α(G n)) 1/n, where α(G n) is the maximum size of an independent set of vertices in G n. We show that there are graphs G and H such that the Shannon capacity of their disjoint union is (much) bigger than the sum of their capacities. This disproves a conjecture of Shannon raised in 1956.