Mine

    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>();	    }