connected(X, Y) :-
    edge(X, Y); edge(Y, X).

path(X, Y, Path) :-
    path(X, Y, [X, Y], P1),
    Path = [X|P1].

path(X, Y, _, Path) :-
    connected(X, Y),
    Path = [Y].

path(X, Y, Visited, Path) :-
    connected(X, Z),
    not(member(Z, Visited)),
    path(Z, Y, [Z|Visited], P1),
    Path = [Z|P1].