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. 2016 Jun 16;17:237. doi: 10.1186/s12859-016-1103-9

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© Limasset et al. 2016

Open Access This 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. 1 — Illustration of the gadget used in the proof of Theorem 1. Encoding a directed graph into a DBG of order 2. The directed graph G (top) admits the same words than the 2-DBG G ^′ (bottom), if we ignore the numbers