Figure 6

Our approach to find an alternative to an optimal integration that creates a bad component. Observe that, from R(A', B) to R(A", B), only the orange edges marked with the symbol ≀ were transformed into the orange edges marked with the symbol $\backslash \backslash$. All the other edges of the diagram were preserved. While the distinct cycles C₃ and C₄ of R(A', B) are merged into a single cycle in R(A", B), the cycle C₂ of R(A',B) is split into two cycles in R(A", B). The hat on markers b and x indicates that we make no assumptions about the orientation of theses markers (but we know they have the same orientation in A' and A"). (i) After the first integration we have a good component ${\mathcal{C}}_1$ at the left side, and a bad component ${\mathcal{C}}_2$ at the right side (at the interval yz...wc...ed...a of A'). The marker y is a link of ${\mathcal{C}}_1$ and ${\mathcal{C}}_2$ and is adjacent to d in genome B. (ii) If we do the optimal integration inside ${\mathcal{C}}_2$, so that y is adjacent to d in genome A", we create the clean 2-cycle ${\mathcal{C}}_2^{\prime }.$ There can be a bad component in R(A", B) (at the interval c...ez...w of A"), but it is strictly smaller than C₂.