A polynomial time algorithm for the triangle packing problem on interval graphs

The triangle packing problem (TPP) is to find the maximum number of pairwise vertex disjoint triangles in a given graph. The TPP is NP-complete in a general graph and even so when a given graph is restricted to a chordal graph. On the other hand, the TPP can be solved in polynomial time for unit int...

Full description

Saved in:
Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 343; pp. 180 - 183
Main Author: Myung, Young-Soo
Format: Journal Article
Language:English
Published: Elsevier B.V 30.01.2024
Subjects:
Interval graph
Packing triangles
Polynomial time algorithm
Interval graph
Packing triangles
Polynomial time algorithm
ISSN:0166-218X
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract The triangle packing problem (TPP) is to find the maximum number of pairwise vertex disjoint triangles in a given graph. The TPP is NP-complete in a general graph and even so when a given graph is restricted to a chordal graph. On the other hand, the TPP can be solved in polynomial time for unit interval graphs. For this reason, it is a well-known open problem to prove whether there exists a polynomial time algorithm solving the TPP on interval graphs. In this paper, we give an answer to the problem.
AbstractList The triangle packing problem (TPP) is to find the maximum number of pairwise vertex disjoint triangles in a given graph. The TPP is NP-complete in a general graph and even so when a given graph is restricted to a chordal graph. On the other hand, the TPP can be solved in polynomial time for unit interval graphs. For this reason, it is a well-known open problem to prove whether there exists a polynomial time algorithm solving the TPP on interval graphs. In this paper, we give an answer to the problem.
Author Myung, Young-Soo
Author_xml – sequence: 1
  givenname: Young-Soo
  surname: Myung
  fullname: Myung, Young-Soo
  email: myung@dankook.ac.kr
  organization: Department of Business Administration, Dankook University, Yongin-si, Gyeonggi-do 16890, Republic of Korea
BookMark eNp9kM1qAyEUhV2k0CTtA3TnC8xUHScd6SqE_kEgmxa6E6PXiemMDiqBvH0N6bqryznwHS7fAs188IDQAyU1JXT1eKyNGmtGWFNyTRiboXnpVxWj3fctWqR0JITQkuZot8ZTGM4-jE4NOLsRsBr6EF0-jNiGiPMBcI5O-X4APCn943yPpxj2A4w4eOx8hngqbB_VdEh36MaqIcH9312ir9eXz817td29fWzW20ozLnJlterAWMXFXoGhLSNGN50AzjvG9qSFRhkgpqVcUM7pijwJ27COg-hsC4I3S0SvuzqGlCJYOUU3qniWlMiLBXmUxYK8WLhUxUJhnq8MlMdODqJM2oHXYFwEnaUJ7h_6Fz3Dac0
Cites_doi 10.1016/j.tcs.2008.02.016
10.1002/net.1975.5.1.45
10.1016/j.disc.2007.07.100
10.1007/s006070170039
ContentType Journal Article
Copyright 2023 Elsevier B.V.
Copyright_xml – notice: 2023 Elsevier B.V.
DBID AAYXX
CITATION
DOI 10.1016/j.dam.2023.10.022
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EndPage 183
ExternalDocumentID 10_1016_j_dam_2023_10_022
S0166218X23003980
GroupedDBID -~X
ADEZE
AFTJW
AI.
ALMA_UNASSIGNED_HOLDINGS
FA8
FDB
OAUVE
VH1
WUQ
AAYXX
CITATION
ID FETCH-LOGICAL-c249t-fca8edfa49baed1520dc389e44822b05e3ade0d514914416079f3284e98f5e943
ISICitedReferencesCount 0
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001108312700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0166-218X
IngestDate Sat Nov 29 07:23:30 EST 2025
Tue Dec 03 03:45:27 EST 2024
IsPeerReviewed true
IsScholarly true
Keywords Interval graph
Packing triangles
Polynomial time algorithm
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c249t-fca8edfa49baed1520dc389e44822b05e3ade0d514914416079f3284e98f5e943
PageCount 4
ParticipantIDs crossref_primary_10_1016_j_dam_2023_10_022
elsevier_sciencedirect_doi_10_1016_j_dam_2023_10_022
PublicationCentury 2000
PublicationDate 2024-01-30
PublicationDateYYYYMMDD 2024-01-30
PublicationDate_xml – month: 01
  year: 2024
  text: 2024-01-30
  day: 30
PublicationDecade 2020
PublicationTitle Discrete Applied Mathematics
PublicationYear 2024
Publisher Elsevier B.V
Publisher_xml – name: Elsevier B.V
References Myung (b7) 2016
Garey, Johnson (b1) 1979
Kloks (b4) 2012
Manić, Wakabayashi (b5) 2008; 308
Karp (b3) 1975; 5
Myung (b6) 2007; 396
Guruswami, Rangan, Chang, Chang, Wong (b2) 2001; 66
Karp (10.1016/j.dam.2023.10.022_b3) 1975; 5
Myung (10.1016/j.dam.2023.10.022_b6) 2007; 396
Manić (10.1016/j.dam.2023.10.022_b5) 2008; 308
Kloks (10.1016/j.dam.2023.10.022_b4) 2012
Guruswami (10.1016/j.dam.2023.10.022_b2) 2001; 66
Myung (10.1016/j.dam.2023.10.022_b7) 2016
Garey (10.1016/j.dam.2023.10.022_b1) 1979
References_xml – year: 2012
  ident: b4
  article-title: Packing Interval Graphs with Vertex-Disjoint Triangles
– volume: 5
  start-page: 45
  year: 1975
  end-page: 68
  ident: b3
  article-title: On the computational complexity of combinatorial problems
  publication-title: Networks
– volume: 396
  start-page: 290
  year: 2007
  end-page: 293
  ident: b6
  article-title: On the clique partition problem in weighted interval graphs
  publication-title: Theoret. Comput. Sci.
– year: 2016
  ident: b7
  article-title: A Counterexample to Ton Kloks’ Polynomial Time Algorithm for Triangle Packing on Interval Graphs
– year: 1979
  ident: b1
  article-title: Computers and Intractability: A Guide to the Theory of NP-Completeness
– volume: 66
  start-page: 79
  year: 2001
  end-page: 89
  ident: b2
  article-title: The
  publication-title: Computing
– volume: 308
  start-page: 1455
  year: 2008
  end-page: 1471
  ident: b5
  article-title: Packing triangles in low degree graphs and indifference graphs
  publication-title: Discrete Math.
– year: 1979
  ident: 10.1016/j.dam.2023.10.022_b1
– volume: 396
  start-page: 290
  year: 2007
  ident: 10.1016/j.dam.2023.10.022_b6
  article-title: On the clique partition problem in weighted interval graphs
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/j.tcs.2008.02.016
– year: 2012
  ident: 10.1016/j.dam.2023.10.022_b4
– volume: 5
  start-page: 45
  issue: 1
  year: 1975
  ident: 10.1016/j.dam.2023.10.022_b3
  article-title: On the computational complexity of combinatorial problems
  publication-title: Networks
  doi: 10.1002/net.1975.5.1.45
– year: 2016
  ident: 10.1016/j.dam.2023.10.022_b7
– volume: 308
  start-page: 1455
  year: 2008
  ident: 10.1016/j.dam.2023.10.022_b5
  article-title: Packing triangles in low degree graphs and indifference graphs
  publication-title: Discrete Math.
  doi: 10.1016/j.disc.2007.07.100
– volume: 66
  start-page: 79
  year: 2001
  ident: 10.1016/j.dam.2023.10.022_b2
  article-title: The Kr-packing problem
  publication-title: Computing
  doi: 10.1007/s006070170039
SSID ssj0001218
ssj0000186
ssj0006644
Score 2.3754425
Snippet The triangle packing problem (TPP) is to find the maximum number of pairwise vertex disjoint triangles in a given graph. The TPP is NP-complete in a general...
SourceID crossref
elsevier
SourceType Index Database
Publisher
StartPage 180
SubjectTerms Interval graph
Packing triangles
Polynomial time algorithm
Title A polynomial time algorithm for the triangle packing problem on interval graphs
URI https://dx.doi.org/10.1016/j.dam.2023.10.022
Volume 343
WOSCitedRecordID wos001108312700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVESC
  databaseName: ScienceDirect database
  issn: 0166-218X
  databaseCode: AIEXJ
  dateStart: 20211207
  customDbUrl:
  isFulltext: true
  dateEnd: 99991231
  titleUrlDefault: https://www.sciencedirect.com
  omitProxy: false
  ssIdentifier: ssj0001218
  providerName: Elsevier
– providerCode: PRVESC
  databaseName: ScienceDirect database
  issn: 0166-218X
  databaseCode: AIEXJ
  dateStart: 20220331
  customDbUrl:
  isFulltext: true
  dateEnd: 99991231
  titleUrlDefault: https://www.sciencedirect.com
  omitProxy: false
  ssIdentifier: ssj0001218
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1ba9RAFB609aE-SLWKVVvmwSeXyJBkkpnHRVuq0Au0hX0LSWambm2TsrtK--_95pJsqC20gi8hDJlDON9w-M6ZcyHkI4srYQyYm9ACDkqc8ajKKzgrPCmZMJnKUuWGTeQHB2IykUdh4ufcjRPIm0ZcX8ur_wo11gC2LZ19BNy9UCzgHaDjCdjxfBDwYzt44cZWG7uKkEs9Ki_O2tl08eOyzym0szqasws9gsf809eju7kyI5f4aLMgsdf1sp4P2evXKYwMWHbPXff7pq89Nd-_CebD2ZHouG2HgYXYJqN0dyQu2vVXxYsPQGZZBFowudP8-kjAOWTaIv84-WwT53zd8a2u1sdWkJUDF4glUrCnZDXOuYRhWh1_25l8H_QAsw3u1rqo2fKSCGQpDa3b_S91l9Yufe_WL9xNOwZU4mSdvAg-AB177F6SJ7p5RZ4PdLlBDsd0iSK1KNIeRQoUKb6lHYo0oEgDirRtaIci9Si-Jqe7Oydf9qIw-yKq4RAvIlOXQitTprIqtQLJYqoGt9TwpuO4YlwnpdJMge5K6xJnLJcmAdXQUhiuZZq8IStN2-i3hJayMgq0rk5rk3IuhGYQZjLDeCV5ojbJp041xZVvcVJ0uX_nBfRYWD3aJehxk6Sd8orA0Tz3KnAG7t_27t-2vSdry5P5gawsZr_0FnlW_15M57PtcFL-AA5vXds
linkProvider Elsevier
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+polynomial+time+algorithm+for+the+triangle+packing+problem+on+interval+graphs&rft.jtitle=Discrete+Applied+Mathematics&rft.au=Myung%2C+Young-Soo&rft.date=2024-01-30&rft.pub=Elsevier+B.V&rft.issn=0166-218X&rft_id=info:doi/10.1016%2Fj.dam.2023.10.022&rft.externalDocID=S0166218X23003980
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0166-218X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0166-218X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0166-218X&client=summon