Fig. 1

Eulerian 2-edge-color multi-graphs for genomes \(A = \big (\{3_{t},1_{t}\},\{1_{h},2_{h}\},\{2_{t},3_{h}\}\big )\), \(\big (\{4_{t}\},\{4_{h},1_{t}\},\{1_{h}\}\big )\), \(B=\big (\{1_{h},2_{h}\},\{2_{t},1_{t}\}\big )\), \(\big (\{3_{t},2_{h}\},\{2_{t},1_{h}\},\{1_{t},3_{h}\}\big )\), and \(A'=\big (\{3_{t},2_{h}\},\{2_{t},1_{t}\},\{1_{h},2_{h}\},\{2_{t},3_{h}\}\big )\), \(\big (\{4_{t}\},\{4_{h},1_{t}\},\{1_{h}\}\big )\). Edges adjacent to a special vertex \(\circ\) represent the endpoints of linear chromosomes (e.g. black edges \(\{1_{h},\circ \}\) and \(\{4_t,\circ \}\)). Extra edges are added for the missing genes (e.g. the black edge \(\{2_{t},2_{h}\}\) and the gray edge \(\{4_h,4_t\}\)), called ghost adjacencies in [15]. In the genomes A and \(A'\), gene 1 is repeated twice, and the operation transforming A into \(A'\) is an insertion of a gene 2, corresponding to the 2-break \(G(A,B)\rightarrow G(A',B)\). A DCJ scenario transforming \(A'\) into the linear genome B includes a deletion of a gene 4