In constraint satisfaction research of artificial intelligence and operations research, constraint graphs and hypergraphs are used to represent relations among constraints in a constraint satisfaction problem. A constraint graph is a special case of a factor graph, which allows for the existence of free variables. In constraint satisfaction research of artificial intelligence and operations research, constraint graphs and hypergraphs are used to represent relations among constraints in a constraint satisfaction problem. A constraint graph is a special case of a factor graph, which allows for the existence of free variables. The constraint hypergraph of a constraint satisfaction problem is a hypergraph in which hyper vertices correspond to the variables and the hyperedges correspond to the constraints. Two hyper vertices are in the same hyperedge if the two variables occur in the same constraint.