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Vertex Deletion Problems on Chordal Graphs

Authors Yixin Cao, Yuping Ke, Yota Otachi, Jie You

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Yixin Cao
Yuping Ke
Yota Otachi
Jie You

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Yixin Cao, Yuping Ke, Yota Otachi, and Jie You. Vertex Deletion Problems on Chordal Graphs. In 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 93, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.FSTTCS.2017.22

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.
Keywords
  • vertex deletion problem
  • maximum subgraph
  • chordal graph
  • (unit) interval graph
  • split graph
  • hereditary property
  • NP-complete
  • polynomial-time algori

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