It is well known that (applying usual notations according to fig. 1) three stage connecting networks with m≥r are non-blocking, if the method of rearrangement is applied, and that at most r-1 reswitchings are necessary. Paull stated that the number of reswitchings may be reduced by increasing the number m of middle switches. He showed that for networks with r=n and m=2n-2, the reswitching of one connection is always sufficient. In the present paper it is shown that for networks with m=2n-2, one reswitching is always sufficient if r≤2n-2. Furthermore it is show that one reswitching is also sufficient in particular networks with m<2n-2. The results of this paper are proved by means of simple considerations and illustrated by examples.
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