%%  Vertex-cover problem 
%%  The graph is given as facts "vtx(X)." and "edge(X,Y)"
%%  and k is the upper bound for vertices in a cover. 
%%  The main predicate is "incover". Atom "incover(X)"
%%  represents the fact that vertex X is in a vertex cover.

% For every vertex, either it is in the cover, or it is not
	{ incover(X) } :- vtx(X).

% Select at least one of the ends of an edge to be included in the cover
	:- edge(X,Y), not incover(X), not incover(Y). 

% The size of the vertex cover is at most k.
 	:- k+1{ incover(X):vtx(X) }.