I am cross posting this question from CS.SE since I believe it is research-related question.
Given a Bayesian Network DAG $G$, we can transform it into a junction tree $T_G$ by performing two steps:
- moralisation (connect variables that have the same child, drop directions)
- triangulation (fill-in edges) i.e chordal graphs.
Are there known conditions/assumptions over $G$ under which for any junction tree $T_G$, $T_G$ will have tree width at most $k$? In other words, bounded treewidth for the triangulated graph of $G$?