Lichen Bao and
Sergey Bereg. Counting Faces in Split Networks. In ISBRA09, Vol. 5251:284-295 of LNCS, 2009.
SplitsTree is a popular program for inferring and visualizing various phylogenetic networks including split networks. Split networks are useful for realizing metrics that are linear combinations of split metrics. We show that the realization is not unique in some cases and design an algorithm for computing split networks with minimum number of faces. We also prove that the minimum number of faces in a split network is equal to the number of pairs of incompatible splits.