Problem
In a directed graph, let P be the second shortest path between two nodes s and t in the graph. To be precise, the length of P is larger than the the shortest path length from s to t but less than or equal to the length of all other s-t paths.
Let v be a node on this path. We will use the notation P(s, v) to denote the sub-path of P from s to v and P(v, t) to denote the sub-path of P from v to t
(a) Prove that at least one of the following statements is true (a) P(s, v) is the shortest path from s to v or (b) P(v, t) is the shortest path from v to t.
(b) Suppose that v is a node such that PO, t) is the shortest path from v to t. What can you say about P(s, v)? I just want a single sentence answer.