title: Any game/graph theory on finite bipartite graph games with perfect information?
body: <p>Suppose you have an undirected, bipartite graph, that consists of vertex sets <em>A</em> and <em>B</em>.</p>
  
  <p>There are two players, <em>P1</em> and <em>P2</em>. <em>P1</em> may start, by picking any vertex <em>V</em> from <em>A</em>.
  Then, <em>P2</em> will choose a vertex <em>W</em> in <em>B</em>, adjacent to <em>V</em>. <em>V</em> will be removed.
  Now, <em>P1</em> can choose another vertex from <em>A</em>, adjacent to <em>W</em>, etc.
  A player wins when he/she was the last one to pick a vertex.</p>
  
  <p>This is a (graph?) game with perfect information. One of the two players will always have a winning strategy.</p>
  
  <p>What existing game/graph theory can be applied, to find which player will win?</p>
  
  <p>I'm trying to create an algorithm that will solve this problem as fast as possible!</p>
  
  <p>I've found a lot of interesting papers on game and graph theory, but none explicitly covered this problem, or theory that can be applied to solve this problem (as far as I know).</p>
  
  <p>Thanks a lot for your knowledge, time and help!</p>