Erdős–Pósa property of obstructions to interval graphs

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

Research output: Contribution to journalArticlepeer-review


A class of graphs (Formula presented.) admits the Erdős–Pósa property if for any graph (Formula presented.), either (Formula presented.) has (Formula presented.) vertex-disjoint “copies” of the graphs in (Formula presented.), or there is a set (Formula presented.) of (Formula presented.) vertices that intersects all copies of the graphs in (Formula presented.). For any graph class (Formula presented.), it is natural to ask whether the family of obstructions to (Formula presented.) has the Erdős–Pósa property. In this paper, we prove that the family of obstructions to interval graphs—namely, the family of chordless cycles and asteroidal witnesses (AWs)—admits the Erdős–Pósa property. In turn, this yields an algorithm to decide whether a given graph (Formula presented.) has (Formula presented.) vertex-disjoint AWs and chordless cycles, or there exists a set of (Formula presented.) vertices in (Formula presented.) that hits all AWs and chordless cycles.

Original languageEnglish
Pages (from-to)702-727
Number of pages26
JournalJournal of Graph Theory
Issue number4
StatePublished - 1 Apr 2023


  • Erdős–Pósa property
  • asteroidal witness
  • interval graphs

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Erdős–Pósa property of obstructions to interval graphs'. Together they form a unique fingerprint.

Cite this