Figure 5. Tree decomposition as generalization of biconnected component decomposition.

At left, the graph used in the SCWRL3 paper is shown along with its biconnected component decomposition. At right, a tree decomposition of the same graph is shown. Residues in blue and green illustrate conditions 2 and 3 of a tree decomposition being satisfied. The relevant conditions are shown below the tree decomposition. At each node of the tree, those residues that are members of set L are shown to the left of the vertical bar, and those of set R are shown to the right. Set L consists of those residues shared with the parent of each node, and R the remaining residues of the node.