Combinatorica

, Volume 18, Issue 3, pp 301–310

The Shannon Capacity of a Union

  • Noga Alon
Original Paper

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.

AMS Subject Classification (1991) Classes:  05C35, 05D10, 94C15 

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Copyright information

© János Bolyai Mathematical Society, 1998

Authors and Affiliations

  • Noga Alon
    • 1
  1. 1.Department of Mathematics, Raymond; and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University; Tel Aviv, Israel; E-mail: noga@math.tau.ac.ilIL

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