Abstract: A mimicking network for a k-terminal network, N, is one whose realizableexternalflows are
the same as those of N. Let S.k/ denote the minimum size of a mimicking network for a k-terminal network.
In this paper we give new constructions of mimicking networks and prove the following results (the values
in brackets are the previously best known results): S.4/ D 5 , S.5/ D 6 . For bounded treewidth
networks we show S.k/ D O.k/ [22k ], and for outerplanar networks we show S.k/ · 10k ¡ 6 [k22kC2].