Erdős–Pósa property of obstructions to interval graphs

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

doi:10.1002/jgt.22895

Erdős–Pósa property of obstructions to interval graphs

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

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	702-727
Number of pages	26
Journal	Journal of Graph Theory
Volume	102
Issue number	4
DOIs	https://doi.org/10.1002/jgt.22895
State	Published - 1 Apr 2023

Keywords

Erdős–Pósa property
asteroidal witness
interval graphs

ASJC Scopus subject areas

Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.1002/jgt.22895

Cite this

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abstract = "A class of graphs (Formula presented.) admits the Erd{\H o}s–P{\'o}sa 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 Erd{\H o}s–P{\'o}sa 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 Erd{\H o}s–P{\'o}sa 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.",

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AU - Zehavi, Meirav

PY - 2023/4/1

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N2 - 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.

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Erdős–Pósa property of obstructions to interval graphs

Abstract

Keywords

ASJC Scopus subject areas

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