title: Hamiltonian Paths in Python with Arbitrary Starting Positions
body: <p>I'm currently working on a project in my spare time where I need to check for the existence of a Hamiltonian path within a graph, however, it doesn't matter where the path begins or ends, only that one exists within the graph.</p>
  <p>I <em>copied</em> this code from another user on here:</p>
  <pre><code>def hamilton(graph, start_v):
    size = len(graph)
    to_visit = [None, start_v]
    path = []
    while(to_visit):
      v = to_visit.pop()
      if v : 
        path.append(v)
        if len(path) == size:
          break
        for x in set(graph[v])-set(path):
          to_visit.append(None)
          to_visit.append(x)
      else:
        path.pop()
    return path
  </code></pre>
  <p>There is obviously a parameter for the starting value. Now my first instinct would be to just iterate the function and run it for every starting vertex, but since I'm going to be running this on graphs with 100+ vertices it would take ages to run to completion. I don't really need to know what the path through all of the vertices is, I just need to know that one exists if that helps.</p>
  <p>How would I adapt this to give an arbitrary starting location?</p>