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 $G$? 
How to go from a DAG model to bounded treewidth?
graph theory;treewidth