Minimum cycle covers of Butterfly and Benes networks

Butterfly network is the most popular bounded-degree derivative of the hypercube network. The benes network consists of back-to-back butterflies. In this paper, we obtain the minimum vertex-disjoint cycle cover number for the odd dimensional butterfly networks and prove that it is not possible to find the same for the even dimensional butterfly networks and benes networks. Further we obtain the minimum edge-disjoint cycle cover number for butterfly networks.