Towards Constant-Factor Approximation for Chordal/Distance-Hereditary Vertex Deletion

For a family of graphs $$\mathcal {F}$$ , Weighted -Deletion is the problem for which input vertex weighted graph $$G = (V, E)$$ and goal to delete $$S \subseteq V$$ with minimum weight such that \setminus S \in \mathcal . Designing constant-factor approximation algorithm large subclasses perfect has been an interesting research direction. Block graphs, 3-leaf power interval are known admit algorithms, but question open chordal distance-hereditary graphs. In this paper, we add one more class list by presenting when intersection They as ptolemaic form superset both block above. Our proof presents new properties algorithmic results on inter-clique digraphs well variant Feedback Vertex Set exploits relationship (named Precedence Constraints), each may be independent interest.