File:ModDecompQuotients.pdf

Summary
The modular decomposition, augmented with quotients. At each node X, the set P of children of X are a partition of X, so they induce a quotient, G[X]/P in G[X]. The nodes of this quotient are P, so the quotient can be represented by installing its edges between the members of P. This is illustrated by the dashed lines connecting siblings. Two graph vertices are adjacent if and only if they are members of two siblings that are adjacent in their parent's quotient; the parent is their least common ancestor.