Fig. 9.

Subgraph with haplotypes: {1,2,3}. Node d must be duplicated, as no more edges can be removed through extension or collapsing without introducing ambiguity. By grouping incoming and outgoing haplotypes on d, the number of duplications can be reduced. In the resulting graph, edges (u,d), (v,d^′), and (w,d^″) can be collapsed. Finally, an extension can be applied to edges (ud,e) and (vd^′,e) which would lead to the null graph. Note that the introduction of grayed out edges is prevented using haplotyping; hence, the edge count is reduced from 6 to 3