:- use_module(library(clpfd)).

vertex(1).
vertex(2).
vertex(3).
link(1, 2).
link(1, 3).
link(2, 3).

arc(X, Y) :- link(X, Y).
arc(X, Y) :- link(Y, X).

coloring(Colors) :- 
    findall(V, vertex(V), Vertices),
    length(Vertices, N),
    same_length(Colors, Vertices),
    Colors ins 0..N, % At most N different colors
    maplist(constrain1(Vertices, Colors), Vertices, Colors),
    sum(Colors, #=, Sum),
    labeling([min(Sum)], [Sum | Colors]).

constrain1(Vertices, Colors, Vertex, Color) :-
    maplist(constrain2(Vertex, Color), Vertices, Colors).
constrain2(V1, C1, V2, C2) :-
    arc(V1, V2), !,
    C1 #\= C2.
constrain2(_, _, _, _).