Fig. 5

Step-wise resolution of a complex of mini-cylces. (i) Starting point. (ii) The mini-cycle complex is highlighted. The complex is created from the mini-cylces \(\{1,2\}\), \(\{2,3\}\), and \(\{2,5\}\). Note that the edges (1, 3) and (5, 3) are not contained in the complex. The best supported directions are between (1, 2). (iii) This direction between (1, 2) is then set. The orange edges are therefore reversed (marked by dashed lines). The adjacency \(\{1,2\}\) is decided and is no longer considered (marked with dark grey). (iv) In this step the best supported direction is (2, 3) and the graph is updated correspondingly. (v) Adjacency \(\{2,5\}\) is left. No direction is superior. Since vertex 2 was solved for previously it is now used. This leads to direction (2, 5). (vi) Then the completed complex is decided and the edges that are contradictionary with the decisions are removed. Note that the circle 3, 4, 5, 3 that was not part of the complex is not removed