# Question: Prove that for any pair of vertices u and v

Prove that for any pair of vertices u and v and any capacity and flow functions c and f, we have cf (u, v) + cf (v, u) = c(u, v) + c(v, u).

**View Solution:**## Answer to relevant Questions

The edge connectivity of an undirected graph is the minimum number k of edges that must be removed to disconnect the graph. For example, the edge connectivity of a tree is 1, and the edge connectivity of a cyclic chain of ...Show that line 7 of INITIALIZE-PREFLOW can be changed to 7 h[s] ← |V [G]| - 2 without affecting the correctness or asymptotic performance of the generic pusher label algorithm.Prove that a comparison network with n inputs correctly sorts the input sequence ¬n, n - 1,..., 1¬ if and only if it correctly sorts the n - 1 zero-one sequences ¬1, 0, 0,..., 0, 0¬, ¬1, 1, ...Give a counterexample to the conjecture that if there is a path from u to v in a directed graph G, then any depth-first search must result in d[v] ≤ f[u].An Euler tour of a connected, directed graph G = (V, E) is a cycle that traverses each edge of G exactly once, although it may visit a vertex more than once. a. Show that G has an Euler tour if and only if in-degree (v) = ...Post your question