It was shown elsewhere by Dantzig that if there exits one complementary tree in the undirected network GG epsilon etan then there exists at least two. The proof there is by means of an algorithm which finds a different complementary tree from a given one. It is shown in this paper that using an extended form of Dantzigs algorithm can lead to a stronger result if there exists one complementary tree in GG epsilon etan then there exists at least four. Also some examples are provided to establish an upper bound on the smallest number of complementary trees in a network GG epsilon etan which has at least one complementary tree.
Sponsored in part by Contract AT(04-3)-326, Grant NSF-GP- 6431. DOI: 10.21236/AD0701309