On the independence number of the strong product of cycle-powers

We determine the independence number of the strong product of cycle-powers C n k and C m p , where C n k denotes the graph obtained from the n -cycle C n by adding all chords joining vertices at most k steps apart on the cycle. The result generalizes a similar result for odd cycles obtained by Hales. The solution is based on the problem of arranging t   1 s and m − t 0s in a circle (where t = ⌊ m k / p ⌋ ) in such a way that every string of p consecutive bits has at most k equal to 1 . A nontrivial lower bound for the Shannon capacity of cycle-powers is obtained on the basis of the independence numbers computed. sult can also be interpreted in terms of packing rectangles into a torus. The maximum number of p -by- k rectangles that can be packed into a two-dimensional m -by- n (rectangular) torus is obtained. The proof of the main theorem can be used to determine the maximum packing itself (or the corresponding largest independent set in the product graph).