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| A hypergraph representation of a constraint satisfaction problem: the constraints are given names (P, Q, R, S, T), and their scopes are shown (P (a, b, c) means that constraint P is on the variables {a, b, c}
| A query decomposition of the problem. Nodes may contain variables, constraints, or both. Although to the rightmost node are associated a total of five variables (i.e. a,b,c,d,e among the two constraints), this is a decomposition of width 3 because no node contains more then three constraints and isolated variables (there is another decomposition of width 2 and it is possible to show that this decomposition og width2 is the minimum with of this hypergraph).
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