  A vexing open problem in information theory is to find the Shannon capacity
of odd cyclic graphs larger than the pentagon and especially for the heptagon.
Lower bounds for the capacity are obtained by solving King chess puzzles. Upper
bounds are obtained by solving entanglement problems, that is to find good
Lovasz umbrellas, quantum state realizations of the graph. We observe that
optimal states are always pure states. The rest is expository. One general
interesting question is whether the Shannon capacity is always some n-th root
of the independence number of the n'th power of the graph.
