Breakpoint graphs and ancestral genome reconstructions

(Top panel) Processing good paths using a -consistent red–blue multi-color. (A) A good path on vertices x₁, x₂,…, x₆ is transformed into a cycle on the same vertices by extending it into x₀, x₁, x₂,…, x₆, x₇ and performing a 2-break on the multi-edges (x₀, x₁) and (x₆, x₇). (B) Transformation of a good cycle on 6 vertices into complete multi-edges with a 2-break on the multi-edges (x₁, x₂), (x₃, x₄) followed by a 2-break on the multi-edges (x₁, x₄), (x₅, x₆). (C) A 2-break on an irregular edge corresponds to a reversal involving chromosome ends. (D) A 2-break on two irregular edges corresponds to a fusion. (Bottom panel) Two ways of transforming a fair edge (x, y) into a good edge: (top) by a 2-break on yellow edges or (bottom) by a 2-break on green edges. In either case, the follow-up processing of the generated simple path results in the same graph with the complete multi-edge (x, y).