On the 2-extendability of planar graphs

Some sufficient conditions for the 2-extendability of k-connected k-regular ( k⩾3) planar graphs are given. In particular, it is proved that for k⩾3, a k-connected k-regular planar graph with each cyclic cutset of sufficiently large size is 2-extendable.

Saved in:
Bibliographic Details
Published inDiscrete mathematics Vol. 96; no. 2; pp. 81 - 99
Main Authors Holton, D.A., Lou, Dingjun, Plummer, Michael D.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 05.12.1991
Elsevier
Subjects
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Sciences and techniques of general use
Extension
Connected graph
Sufficient condition
Planar graph
Cut set
Online AccessGet full text

Cover

Abstract Some sufficient conditions for the 2-extendability of k-connected k-regular ( k⩾3) planar graphs are given. In particular, it is proved that for k⩾3, a k-connected k-regular planar graph with each cyclic cutset of sufficiently large size is 2-extendable.
AbstractList Some sufficient conditions for the 2-extendability of k-connected k-regular ( k⩾3) planar graphs are given. In particular, it is proved that for k⩾3, a k-connected k-regular planar graph with each cyclic cutset of sufficiently large size is 2-extendable.
Author Holton, D.A.
Lou, Dingjun
Plummer, Michael D.
Author_xml – sequence: 1
  givenname: D.A.
  surname: Holton
  fullname: Holton, D.A.
– sequence: 2
  givenname: Dingjun
  surname: Lou
  fullname: Lou, Dingjun
– sequence: 3
  givenname: Michael D.
  surname: Plummer
  fullname: Plummer, Michael D.
  organization: Department of Mathematics, Vanderbilt University, Nashville, TN 37235, USA
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=5057235$$DView record in Pascal Francis
BookMark eNp9j01LAzEQQINUsK3-Aw97ENTDapLdfOxFkOIXFHqoQm9hmp3YyJpdkkXsv3drpUdPw8B7M7wJGYU2ICHnjN4wyuQtpYznhRSrq4pdV5RzlS-PyJhpxXOp2WpExgfkhExS-qDDLgs9JpeLkPUbzHiO3z2GGta-8f02a13WNRAgZu8Ruk06JccOmoRnf3NK3h4fXmfP-Xzx9DK7n-eWC9rnhbOiLLHmYAF0IWS5lgKsXGsoOGeKISptmZCKK1dbRyuNtaNQMS6cqKCYknJ_18Y2pYjOdNF_QtwaRs0u1uxKzK7EVMz8xprloF3stQ6ShcZFCNangyuoULwQA3a3x3BI-PIYTbIeg8XaR7S9qVv__58fS81pUw
CODEN DSMHA4
CitedBy_id crossref_primary_10_1007_s00373_019_02048_9
crossref_primary_10_1007_s10114_013_2255_4
crossref_primary_10_1002_jgt_3190170213
crossref_primary_10_1080_17445760_2019_1659259
crossref_primary_10_1016_0012_365X_92_00485_A
crossref_primary_10_1016_j_tcs_2022_05_028
crossref_primary_10_1007_s10910_017_0806_0
crossref_primary_10_4236_am_2013_42053
crossref_primary_10_1016_j_disc_2007_04_055
crossref_primary_10_1016_0012_365X_95_00196_4
crossref_primary_10_1016_j_disc_2009_04_017
crossref_primary_10_1002_jgt_22764
crossref_primary_10_1007_s10878_014_9759_4
crossref_primary_10_1142_S1793830911001322
crossref_primary_10_1016_0012_365X_92_90292_N
crossref_primary_10_1007_s10878_010_9304_z
crossref_primary_10_1007_s10878_012_9472_0
Cites_doi 10.1016/0012-365X(80)90037-0
10.1016/0095-8956(83)90067-9
ContentType Journal Article
Copyright 1991
1992 INIST-CNRS
Copyright_xml – notice: 1991
– notice: 1992 INIST-CNRS
DBID 6I.
AAFTH
IQODW
AAYXX
CITATION
DOI 10.1016/0012-365X(91)90227-S
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
Pascal-Francis
CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1872-681X
EndPage 99
ExternalDocumentID 10_1016_0012_365X_91_90227_S
5057235
0012365X9190227S
GroupedDBID --K
--M
-DZ
-~X
.DC
.~1
0R~
1B1
1RT
1~.
1~5
29G
4.4
41~
457
4G.
5GY
5VS
6I.
6OB
6TJ
7-5
71M
8P~
9JN
AACTN
AAEDT
AAEDW
AAFTH
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AASFE
AAXUO
ABAOU
ABEFU
ABFNM
ABJNI
ABMAC
ABTAH
ABVKL
ABXDB
ABYKQ
ACAZW
ACDAQ
ACGFS
ACRLP
ADBBV
ADEZE
ADIYS
ADMUD
AEBSH
AEKER
AENEX
AEXQZ
AFFNX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AI.
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
ARUGR
ASPBG
AVWKF
AXJTR
AZFZN
BKOJK
BLXMC
CS3
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
FA8
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
GBLVA
HVGLF
HZ~
IHE
IXB
J1W
KOM
M26
M41
MHUIS
MO0
MVM
N9A
NCXOZ
O-L
O9-
OAUVE
OK1
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
RNS
ROL
RPZ
SDF
SDG
SDP
SES
SEW
SPC
SPCBC
SSW
SSZ
T5K
TN5
UPT
VH1
WH7
WUQ
XJT
XOL
XPP
ZCG
ZMT
ZY4
~G-
6XO
AALMO
AAPBV
ABFLS
ABPIF
ABPTK
ADALY
IPNFZ
IQODW
0SF
AAXKI
AAYXX
ADVLN
AFJKZ
AKRWK
CITATION
ID FETCH-LOGICAL-c250t-3fc544ed2acaa83564b65ac6b8a322171ee78c156727fdcf098edf0a9125f59a3
IEDL.DBID ABVKL
ISSN 0012-365X
IngestDate Thu Sep 26 18:12:58 EDT 2024
Fri Nov 25 01:06:23 EST 2022
Fri Feb 23 02:29:27 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords Extension
Connected graph
Sufficient condition
Planar graph
Cut set
Language English
License http://www.elsevier.com/open-access/userlicense/1.0
CC BY 4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c250t-3fc544ed2acaa83564b65ac6b8a322171ee78c156727fdcf098edf0a9125f59a3
OpenAccessLink https://www.sciencedirect.com/science/article/pii/0012365X9190227S
PageCount 19
ParticipantIDs crossref_primary_10_1016_0012_365X_91_90227_S
pascalfrancis_primary_5057235
elsevier_sciencedirect_doi_10_1016_0012_365X_91_90227_S
PublicationCentury 1900
PublicationDate 1991-12-05
PublicationDateYYYYMMDD 1991-12-05
PublicationDate_xml – month: 12
  year: 1991
  text: 1991-12-05
  day: 05
PublicationDecade 1990
PublicationPlace Amsterdam
PublicationPlace_xml – name: Amsterdam
PublicationTitle Discrete mathematics
PublicationYear 1991
Publisher Elsevier B.V
Elsevier
Publisher_xml – name: Elsevier B.V
– name: Elsevier
References Plummer (BIB7) 1980; 31
Plummer (BIB8) 1989; 41
Thomassen (BIB9) 1983; 35
Harary (BIB2) 1969
Lou, Holton (BIB5) 1988
Bondy, Murty (BIB1) 1976
Holton, Plummer (BIB4) 1988
Holton, Plummer (BIB3) 1987; 52
Lovász, Plummer (BIB6) 1986; 29
Holton (10.1016/0012-365X(91)90227-S_BIB3) 1987
Thomassen (10.1016/0012-365X(91)90227-S_BIB9) 1983; 35
Bondy (10.1016/0012-365X(91)90227-S_BIB1) 1976
Plummer (10.1016/0012-365X(91)90227-S_BIB8) 1989; 41
Lou (10.1016/0012-365X(91)90227-S_BIB5) 1988
Lovász (10.1016/0012-365X(91)90227-S_BIB6) 1986; 29
Harary (10.1016/0012-365X(91)90227-S_BIB2) 1969
Holton (10.1016/0012-365X(91)90227-S_BIB4) 1988
Plummer (10.1016/0012-365X(91)90227-S_BIB7) 1980; 31
References_xml – volume: 31
  start-page: 201
  year: 1980
  end-page: 210
  ident: BIB7
  article-title: On
  publication-title: Discrete Math.
  contributor:
    fullname: Plummer
– year: 1976
  ident: BIB1
  article-title: Graph Theory with Applications
  contributor:
    fullname: Murty
– volume: 52
  start-page: 281
  year: 1987
  end-page: 300
  ident: BIB3
  article-title: 2-extendability in 3-polytopes
  publication-title: Colloq. Math. Soc. J. Bolyai
  contributor:
    fullname: Plummer
– volume: 41
  start-page: 347
  year: 1989
  end-page: 354
  ident: BIB8
  article-title: A theorem on matchings in the plane
  publication-title: Graph Theory in Memory of G.A. Dirac
  contributor:
    fullname: Plummer
– year: 1969
  ident: BIB2
  article-title: Graph Theory
  contributor:
    fullname: Harary
– year: 1988
  ident: BIB4
  article-title: Matching extension and connectivity in graphs II
  publication-title: Proc. Sixth International Conference on the Theory and Applications of Graphs
  contributor:
    fullname: Plummer
– year: 1988
  ident: BIB5
  publication-title: Lower bound of cyclic edge connectivity for
  contributor:
    fullname: Holton
– volume: 35
  start-page: 129
  year: 1983
  end-page: 141
  ident: BIB9
  article-title: Girth in graphs
  publication-title: J. Combin. Theory Ser. B
  contributor:
    fullname: Thomassen
– volume: 29
  year: 1986
  ident: BIB6
  article-title: Matching theory
  publication-title: Ann. Discrete Math.
  contributor:
    fullname: Plummer
– volume: 41
  start-page: 347
  year: 1989
  ident: 10.1016/0012-365X(91)90227-S_BIB8
  article-title: A theorem on matchings in the plane
  contributor:
    fullname: Plummer
– volume: 31
  start-page: 201
  year: 1980
  ident: 10.1016/0012-365X(91)90227-S_BIB7
  article-title: On n-extendable graphs
  publication-title: Discrete Math.
  doi: 10.1016/0012-365X(80)90037-0
  contributor:
    fullname: Plummer
– year: 1976
  ident: 10.1016/0012-365X(91)90227-S_BIB1
  contributor:
    fullname: Bondy
– year: 1969
  ident: 10.1016/0012-365X(91)90227-S_BIB2
  contributor:
    fullname: Harary
– year: 1988
  ident: 10.1016/0012-365X(91)90227-S_BIB5
  publication-title: Lower bound of cyclic edge connectivity for n-extendability of regular graphs
  contributor:
    fullname: Lou
– volume: 29
  year: 1986
  ident: 10.1016/0012-365X(91)90227-S_BIB6
  article-title: Matching theory
  contributor:
    fullname: Lovász
– year: 1988
  ident: 10.1016/0012-365X(91)90227-S_BIB4
  article-title: Matching extension and connectivity in graphs II
  contributor:
    fullname: Holton
– start-page: 281
  year: 1987
  ident: 10.1016/0012-365X(91)90227-S_BIB3
  article-title: 2-extendability in 3-polytopes
  contributor:
    fullname: Holton
– volume: 35
  start-page: 129
  year: 1983
  ident: 10.1016/0012-365X(91)90227-S_BIB9
  article-title: Girth in graphs
  publication-title: J. Combin. Theory Ser. B
  doi: 10.1016/0095-8956(83)90067-9
  contributor:
    fullname: Thomassen
SSID ssj0001638
Score 1.4597471
Snippet Some sufficient conditions for the 2-extendability of k-connected k-regular ( k⩾3) planar graphs are given. In particular, it is proved that for k⩾3, a...
SourceID crossref
pascalfrancis
elsevier
SourceType Aggregation Database
Index Database
Publisher
StartPage 81
SubjectTerms Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Sciences and techniques of general use
Title On the 2-extendability of planar graphs
URI https://dx.doi.org/10.1016/0012-365X(91)90227-S
Volume 96
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3PS8MwFA5uuygi_sSpGz0I6iFsTZu2OW7imD-mhznpLby0CQykK9s8-N-bNG3ZDiJ4KSSQpHxtvvfl8fIeQtc-BZDQZ1iQKMW-qwQWbmAexushExYmxqE_eQ3GM_8ppvHGXRgTVllyv-X0gq3Lnl6JZi-fz3s2-xiNmTZphITTBmoRLX715mwNhh_PLzUfG8Vh-ZhgM6C6QOcGvbrvlrl3xTR4-puB2s9hpWFTtt7FhhEaHaKDUj06A_uCR2hHZsdob1KnXl2doJu3zNFNh2Dr37Z5uL-dhXLyT8hg6RQ5qlenaDZ6eL8f47IaAk60TFljTyXU92VKIAHQuinwRUAhCUQEelO6oStlGCX6OKYViUoT1WeRTFUfmJYwijLwzlAzW2TyHDnarFMt5ESQSuIDuOBFVAgVmAqDSgBtI1xBwHOb9IJX0WAGMm4g48zlBWR82kZhhRPf-nhc8_IfIztbsNbLmXMT8ejFv2e-RLtFVJeJPKFXqLlefsmO1g9r0S1_kC5qPMbDHzj8v5E
link.rule.ids 315,783,787,3513,27581,27936,27937,45675,45886
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3PS8MwFA46Dyoi_sSp0x4E9RC2pk3aHlUcm27zsA16Cy9tAgPpyjYP_vcmTVu2gwheCg1tWr6m3_vyeD8QuvMpgIROhAUJU-y7SmDhMnMwXg-ZREFiHPrDEetN_beYxmu5MCassuR-y-kFW5cj7RLNdj6btW31MRpH2qQREoy30Y7JujSrvB8_12xs9IZlY4LN5VX6nMva9dhD5D4Wk-Dxb-bpIIelBk3ZbhdrJqh7hA5L7eg82dc7RlsyO0H7w7rw6vIU3X9kjj51CLbebVuF-9uZKyf_hAwWTlGhenmGpt3XyUsPl70QcKJFygp7KqG-L1MCCYBWTcwXjELCRAj6l3QDV8ogTPRmTOsRlSaqE4UyVR2ItIBRNALvHDWyeSYvkKONOtUyTrBUEh_ABS-kQihm-gsqAbSJcAUBz23JC17FghnIuIGMRy4vIOPjJgoqnPjGp-Oalf-4s7UBa_04s2siHr3898y3aLc3GQ74oD96v0J7RXyXiUGh16ixWnzJllYSK3FTLJUf2p3AYQ
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=On+the+2-extendability+of+planar+graphs&rft.jtitle=Discrete+mathematics&rft.au=HOLTON%2C+D.+A&rft.au=LOU%2C+D&rft.date=1991-12-05&rft.pub=Elsevier&rft.issn=0012-365X&rft.eissn=1872-681X&rft.volume=96&rft.issue=2&rft.spage=81&rft.epage=99&rft_id=info:doi/10.1016%2F0012-365X%2891%2990227-S&rft.externalDBID=n%2Fa&rft.externalDocID=5057235
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0012-365X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0012-365X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0012-365X&client=summon