Extension to cographs and trees

Determine whether analogous metric, embedding, and computational-complexity results hold for the quotient graph-edit distances on cographs and on trees.

Background

The paper’s analysis of cluster graphs depends on representing block alignments by contingency tables and on the resulting transportation formulation. Cographs and trees do not possess the same block-structure correspondence in the methods developed here.

The authors therefore identify the corresponding questions for these two graph classes as open, without asserting a specific conjectured outcome.