Vertex Deletion Problems on Chordal Graphs

TL;DR

This paper systematically studies vertex deletion problems on chordal graphs, providing polynomial algorithms or NP-completeness proofs for many cases, including the NP-completeness of deleting vertices from chordal to interval graphs.

Contribution

It offers a comprehensive complexity classification for vertex deletion problems within subclasses of chordal graphs, extending prior general results.

Findings

Polynomial-time algorithms for certain vertex deletion problems

NP-completeness proofs for others, including chordal to interval graphs

Complete dichotomy for vertex deletion problems on chordal subclasses

Abstract

Containing many classic optimization problems, the family of vertex deletion problems has an important position in algorithm and complexity study. The celebrated result of Lewis and Yannakakis gives a complete dichotomy of their complexity. It however has nothing to say about the case when the input graph is also special. This paper initiates a systematic study of vertex deletion problems from one subclass of chordal graphs to another. We give polynomial-time algorithms or proofs of NP-completeness for most of the problems. In particular, we show that the vertex deletion problem from chordal graphs to interval graphs is NP-complete.