Graph Coloring in Prolog: what am I doing wrong?

Question

I'm writing a Prolog program for a simple skill, coloring a graph. I have done everything that I had on my checklist to do: make a graph using a list of edges, make color facts, make color bindings, assign colors, check for conflicts, etc. It always returns false! I keep trying to tweak it slightly , but nothing is working:

color(red).
color(green).
color(blue).
color(yellow).
color(purple).
color(brown).

edge(A,A) :- [A,A].

cb(Item,Color).

graph([edge(A,A)]).

vertex(A,B) :- edge(A,B) ; edge(B,A).

colorItem([],[]).
colorItem([Item|Items], [Binding|Bindings]) :-
    colorItem(Items, Bindings),
    Binding = cb(Item, Color),
    color(Color),
    noconflict(Binding, Bindings).

colorGraph(Graph, Bindings) :- colorItem(Graph,Bindings).

noconflict(_,[]).
noconflict(Cb1,[Cb2|Cbs]) :- not(conflict(Cb1,Cb2)), noconflict(Cb1,Cbs).

conflict(cb(N1,Color), cb(N2,Color)) :- vertex(N1,N2).

It should look like something like this IIRC:

?- colorGraph([edge(ny,nj)], Bindings).
Bindings = [cb(nj, green), cb(ny, red)] ;
Bindings = [cb(nj, blue), cb(ny, red)] ;
Bindings = [cb(nj, yellow), cb(ny, red)] .

But I get this:

?- colorGraph([edge(ny,nj)], Bindings).
Bindings = [cb(edge(ny, nj), red)] 
Bindings = [cb(edge(ny, nj), green)] 
Bindings = [cb(edge(ny, nj), blue)] 
Bindings = [cb(edge(ny, nj), yellow)] 
Bindings = [cb(edge(ny, nj), purple)] 
Bindings = [cb(edge(ny, nj), brown)].

There's something obvious and important that I'm missing with my edges and graph. Any advice or tips would be appreciated.

Answer 1

Replace:

colorGraph(graph, bindings) :- colorItem(graph,bindings).

With:

colorGraph(Graph, Bindings) :- colorItem(Graph, Bindings).

Variables start with either an underscore or an upper case letter in Prolog. Same issue apparently with some of the other predicates.