Resolution:
## Figure 5.
Running example for the proof of Theorem 1. A running example for the proof of Theorem 1 where T is a tree in the instance tuple I, S is an assumed solution for , and R = Γ(S, X, w). Highlighted regions in T are the edge partitions E_{1}, E_{2}, and E_{3}. The rest of edges form the partition E_{4}. By counting the costs for each partition we have Σ_{1} =6 - 4 = 2, Σ_{2} =1 - 3 = −2, Σ_{3} = 2 − 1 = 1, and Σ_{4} =3 − 3 = 0. Overall we have DC(T, S) − DC(T, R) = 1.
Lin |