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. 2019 Jul 27;14:17. doi: 10.1186/s13015-019-0152-9

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© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

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Fig. 4 — a $T_{1}$ and $T_{2}$ before applying the first step from Observation 4, b $T_{1}^{'}$ and $T_{2}^{'}$ obtained from $T_{1}$ and $T_{2}$ from a after first step of deleting vertices which do not belong to paths between root and crucial vertices, c the resulting tree ${\tilde{T}}_{1} = {\tilde{T}}_{2}$ after applying second step