Fig. 13

Proper unrooted phylogenetic network N^u (consisting of one non-trivial blob and two trivial blobs (leaves)) that is binary and chordal. After deleting its leaves, it can be reduced to a single edge by a sequence of vertex suppression and edge deletion operations. First, we consider the triangle uvx and suppress u. This results in a parallel edge between v and x, which gets deleted. Then, the triangle vwx is considered and w is suppressed. Deleting the resulting parallel edge between v and x leads to a single edge. This implies that N^u is edge-based