Correction to: Tree-Based Unrooted Phylogenetic Networks

Correction to: Bull Math Biol (2018) 80:404–416

The level-5 example of a network presented in Fig. 4 of Francis et al. (2018) is tree-based even though it states in the caption and in the text that this is not the case. This is because it contains the spanning tree with leaf-set \(\{x,y\}\) given by the path \(x, a, v_1, v_2, e, f, g, h, b, c, d, y\). The example should be replaced by the network in Fig. 1, which is level-5 and not tree-based. The network in Fig. 1 is not tree-based since any spanning tree with leaf-set \(\{x,y\}\) must contain the edges \(\{x,a\}\) and \(\{d,y\}\) as well as one of the paths \(b,h,h^{\prime },c\) or \(b,h^{\prime },h,c\) and one of the paths \(f,g,g^{\prime },e\) or \(f,g^{\prime },g,e\). It follows that the spanning tree then must also contain the edges \(\{a,b\}\), \(\{c,d\}\), \(\{a,f\}\), and \(\{e,d\}\), which is impossible. We thank Remie Janssen and Yukihiro Murakami for bringing this issue and replacement example to our attention.

Fig. 1

A level-5 network that is not tree-based

Since drafting this erratum, other authors have independently pointed out the same error and made a more comprehensive corresponding fix (Fischer et al. 2018).


  1. Fischer M, Galla M, Herbst L, Long Y, Wicke K (2018) Non-binary treebased unrooted phylogenetic networks and their relations to binary and rooted ones. Preprint, arXiv:1810.06853v1, 16th Oct 2018

  2. Francis A, Huber KT, Moulton V (2018) Tree-based unrooted phylogenetic networks. Bull Math Biol 80:404–416

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Correspondence to K. T. Huber.

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Francis, A., Huber, K.T. & Moulton, V. Correction to: Tree-Based Unrooted Phylogenetic Networks. Bull Math Biol 81, 936–937 (2019).

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