Correction to: Classes of tree-based networks

Correction to: Vis Comput Ind Biomed Art 3, 12 (2020)

https://doi.org/10.1186/s42492-020-00043-z

Following publication of the original article [1], in the description of the leaf shrinking procedure as well as in Algorithm 1 and the definition of edge-based graphs in [1], the condition that G contains at least two leaves (i.e., the condition |V_L(G)| ≥ 2) needs to be omitted. Moreover, in line 2 of Algorithm 1 it should read $\left|V\left(\mathcal{LS}\left(G\right)\right)\right|>2$.

In particular, Algorithm 1 and Definition 3 should read as follows:

Definition 3 Let G be a connected graph with |V(G)| ≥ 2. If the leaf shrink graph $\mathcal{LS}\left(G\right)$ of G is a single edge, G is called edge-based. Else, G is called non-edge-based. If G = N^u is a proper phylogenetic network with |V(N^u)| ≥ 2 and |X| ≥ 2 and $\mathcal{LS}\left(N^u\right)$ is a single edge, we call N^u an edge-based network. Else, N^u is called non-edge-based.

We thank Tom Niklas Hamann for bringing this issue to our attention.