Figure 5

Relating 1-MCP _c and 1-MCP _ℓ . (a) The breakpoint graph $B=B\left(\mathcal{G},{\mathcal{A}}_c\right)$; black edges are $A\left({\mathcal{A}}_c\right)$ and and gray edges are $A\left(\mathcal{G}\right)$. The edge e = {1 _t , 6 _h } is the only edge in $A\left({\mathcal{A}}_c\right)\backslash A\left({\mathcal{A}}_{\ell }\right)$. Since e is not in a cycle component of B, we have θ(e) = 1. (b) The breakpoint graph $B^{\prime }=B\left({\mathcal{G}}_c,{\mathcal{A}}_c\right)$, where ${\mathcal{G}}_c$ is a completion of $\mathcal{ G}$ and a solution to 1-MCP _c . The adjacency f is in $A\left({\mathcal{G}}_c\right)$ and shown by a gray dashed edge. B' has two cycles, and removing e and f decreases the number of cycles by one.