Feedback vertex set inspired kernel for chordal vertex deletion

Akanksha Agrawal, Daniel Lokshtanov, Pranabendu Misra, Saket Saurabh, Meirav Zehavi

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

Given a graph G and a parameter k, the Chordal Vertex Deletion (CVD) problem asks whether there exists a subset U ⊆ V(G) of size at most k that hits all induced cycles of size at least 4. The existence of a polynomial kernel for CVD was a well-known open problem in the field of Parameterized Complexity. Recently, Jansen and Pilipczuk resolved this question affirmatively by designing a polynomial kernel for 1 CVD of size O(k 161 log 58 k) and asked whether one can design a kernel of size O(k 10 ) [Jansen an Pilipczuk, SODA 2017]. While we do not completely resolve this question, we design a significantly smaller kernel of size O(k 12 log 10 k), inspired by the O(k 2 )-size kernel for Feedback Vertex Set [Thomassé, TALG 2010]. Furthermore, we introduce the notion of the independence degree of a vertex, which is our main conceptual contribution.

Original languageEnglish
Article numbera11
JournalACM Transactions on Algorithms
Volume15
Issue number1
DOIs
StatePublished - 1 Dec 2018

Keywords

  • Chordal graph
  • Chordal vertex deletion
  • Kernelization
  • Parameterized complexity

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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