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@@ -869,6 +869,22 @@ singletons constructed according to the following rules: were assigned to parts when its children were handled. \end{enumerate} +\begin{figure} + \centering + \def\svgwidth{\columnwidth} + \input{partition.pdf_tex} + \caption{ + An LCA-partition of the tree with respect to the black vertices. The + dark grey vertices are added when computing the LCA closure, the light + grey vertices are the final vertices needed to create a minimal + partition ready set containing the black vertices. Part (a) is an + example of a singleton, part (b) of a subtree with a hole, and (c) of a + subtree. + }\label{partition-figure} +\end{figure} + +See Figure \ref{partition-figure} for an example of a partitioned tree. + If $W$ is not parition ready, we will define the LCA partition with respect to $W$ the partition with respect to the minimal partition ready set that contains $W$. Skipping ahead, the LCA partition of the set of vertices relabeled in a |