A Constraint Model for the Tree Decomposition of a Graph

We present a constraint model for the problem of producing a tree decomposition of a graph. The inputs to the model are a simple graph G, the number of nodes in the desired tree decomposition and the maximum cardinality of each node in that decomposition. Via a sequence of decision problems, the model allows us to find the tree width of a graph whilst delivering a tree decomposition of that width, i.e. a witness.