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# the primal graph is [[Chordal graph|chordal]];
# the variables of every [[maximal clique]] of the primal graph are the scope of a constraint and vice versa; this property is called ''conformality''.
In turn, chordality can be checked using a [[max-cardinality ordering]] of the variables. Such an ordering can also be used, if the two conditions above are met, for finding a join tree of the problem. Ordering constraints by their highest variable according to the ordering, an algorithm for producing a join tree proceeds from the last to the first constraint; at each step, a constraint is connected to the constraint that shares a maximal number of variables with it among the constraints that precede it in the ordering.
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