% guess
in(X) v out(X) :- node(X).

% enforce condition 1
:- in(X), in(Y), monochrome_path(X,Y,C).

% auxiliary predicate
monochrome_path(X,Y,C) :- edge(X,Y,C).
monochrome_path(X,Y,C) :- monochrome_path(X,Z,C), edge(Z,Y,C).


% enforce condition 2
connected(X) :- edge(X, A, B), in(Y), monochrome_path(X,Y,C), X != Y.
:- out(X), not connected(X).