The Shannon Capacity of a Union
- Cite this article as:
- Alon, N. Combinatorica (1998) 18: 301. doi:10.1007/PL00009824
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For an undirected graph \(\), let \(\) denote the graph whose vertex set is \(\) in which two distinct vertices \(\) and \(\) are adjacent iff for all i between 1 and n either \(\) or \(\). The Shannon capacity c(G) of G is the limit \(\), where \(\) is the maximum size of an independent set of vertices in \(\). 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.