public LinkedList<Integer> BFS(UndirectedGraph g, int start, int goal) { 
    	Queue<LinkedList<Integer>> routes = new ArrayDeque<LinkedList<Integer>>(g.numVertices());
    	LinkedList<Integer> vertices = new LinkedList<Integer>();
    	vertices.add(new Integer(start));
    	while (!routes.isEmpty()) {
    		LinkedList<Integer> currentRoute = routes.poll();
    		int currentVertex = currentRoute.poll();
    		VertexIterator vi = g.adjacentVertices(currentVertex);
			while(vi.hasNext()) {
				int adjacentVertex = vi.next();
				LinkedList<Integer> newRoute;
				newRoute = currentRoute;
				newRoute.add(adjacentVertex);
				routes.add(newRoute);
				if(adjacentVertex == goal) {
					return newRoute;
				}
			}
    	}
		return new LinkedList<Integer>();	
    }