Some Remarks on the Shannon Capacity of Odd Cycles

Abstract

We tackle the problem of estimating the Shannon capacity of cycles of odd length. We present some strategies which allow us to find tight bounds on the Shannon capacity of cycles of various odd lengths, and suggest that the difficulty of obtaining a general result may be related to different behaviours of the capacity, depending on the “structure” of the odd integer representing the cycle length. We also describe the outcomes of some experiments, from which we derive the evidence that the Shannon capacity of odd cycles is extremely close to the value of the Lovasz theta function.