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	Accepted/In press - 1 Jan 2022

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

@article{cdebcaf8abdb41b692586792a8f107d9,

title = "Erd{\H o}s–P{\'o}sa property of obstructions to interval graphs",

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.",

keywords = "Erd{\H o}s–P{\'o}sa property, asteroidal witness, interval graphs",

author = "Akanksha Agrawal and Daniel Lokshtanov and Pranabendu Misra and Saket Saurabh and Meirav Zehavi",

note = "Funding Information: A preliminary version of this paper appeared in the proceedings of STACS 2018. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 819416, 306992, and 715744), from the Israel Science Foundation (ISF) under the Individual Research Grant program (grant no. 1176/18), and from the PBC Program of Fellowships for Outstanding Post‐doctoral Researchers from China and India (no. 5101479000). Publisher Copyright: {\textcopyright} 2022 Wiley Periodicals LLC.",

year = "2022",

month = jan,

day = "1",

doi = "10.1002/jgt.22895",

language = "English",

volume = "102",

pages = "702--727",

journal = "Journal of Graph Theory",

issn = "0364-9024",

publisher = "Wiley-Liss Inc.",

number = "4",

}

TY - JOUR

T1 - Erdős–Pósa property of obstructions to interval graphs

AU - Agrawal, Akanksha

AU - Lokshtanov, Daniel

AU - Misra, Pranabendu

AU - Saurabh, Saket

AU - Zehavi, Meirav

N1 - Funding Information: A preliminary version of this paper appeared in the proceedings of STACS 2018. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 819416, 306992, and 715744), from the Israel Science Foundation (ISF) under the Individual Research Grant program (grant no. 1176/18), and from the PBC Program of Fellowships for Outstanding Post‐doctoral Researchers from China and India (no. 5101479000). Publisher Copyright: © 2022 Wiley Periodicals LLC.

PY - 2022/1/1

Y1 - 2022/1/1

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.

AB - 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.

KW - Erdős–Pósa property

KW - asteroidal witness

KW - interval graphs

UR - http://www.scopus.com/inward/record.url?scp=85138907044&partnerID=8YFLogxK

U2 - 10.1002/jgt.22895

DO - 10.1002/jgt.22895

M3 - Article

AN - SCOPUS:85138907044

SN - 0364-9024

VL - 102

SP - 702

EP - 727

JO - Journal of Graph Theory

JF - Journal of Graph Theory

IS - 4

ER -

Erdős–Pósa property of obstructions to interval graphs

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this