A 4-colorable mapping for a class of crosstalkfree permutations in dilated networks for photonic switching

In order to reduce the impact of crosstalk in optical switching, dilated architectures can be adopted to build interconnection networks. This approach, that avoids the necessity of optical buffers, is considered here for the development of 4-layered switches, based on the Omega topology. In particular, the correlation existing between the crosstalk-free configurations of the switch and the 4- colorability properties of the correspondent permutation graphs is demonstrated. Then, the theorems presented in this paper allow to define a method to identify either such crosstalk-free configurations, or their relative optimal permutations partitions.