title: algorithm - shortest path from vertex a to b containing vertex v
body: <p>I'm having trouble trying to figure out a shortest-path algorithm such that given a undirected unweighted graph with an start point a and end point b, every path must contain/run into the vertex v. 
  Is it possible to get it in O(n) if the length is greater than n / 2?</p>
  
  <p>I found this <a href="https://stackoverflow.com/questions/222413/find-the-shortest-path-in-a-graph-which-visits-certain-nodes">question</a> but it didn't spark anything in my head. It did get me thinking about BFS but how would I know when I went through vertex v?</p>
  
  <p>Can anyone point me into some direction?
  Thanks!</p>