List-k-Coloring H-Free Graphs for All k>4
Given an integer k > 4 and a graph H , we prove that, assuming P ≠ NP, the List- k -Coloring Problem restricted to H -free graphs can be solved in polynomial time if and only if either every component of H is a path on at most three vertices, or removing the isolated vertices of H leaves an induc...
Uloženo v:
| Vydáno v: | Combinatorica (Budapest. 1981) Ročník 44; číslo 5; s. 1063 - 1068 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2024
Springer Nature B.V |
| Témata: | |
| ISSN: | 0209-9683, 1439-6912 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Given an integer
k
>
4
and a graph
H
, we prove that, assuming P
≠
NP, the
List-
k
-Coloring Problem
restricted to
H
-free graphs can be solved in polynomial time if and only if either every component of
H
is a path on at most three vertices, or removing the isolated vertices of
H
leaves an induced subgraph of the five-vertex path. In fact, the “if” implication holds for all
k
≥
1
. |
|---|---|
| AbstractList | Given an integer
k
>
4
and a graph
H
, we prove that, assuming P
≠
NP, the
List-
k
-Coloring Problem
restricted to
H
-free graphs can be solved in polynomial time if and only if either every component of
H
is a path on at most three vertices, or removing the isolated vertices of
H
leaves an induced subgraph of the five-vertex path. In fact, the “if” implication holds for all
k
≥
1
. Given an integer k>4 and a graph H, we prove that, assuming P≠NP, the List-k-Coloring Problem restricted to H-free graphs can be solved in polynomial time if and only if either every component of H is a path on at most three vertices, or removing the isolated vertices of H leaves an induced subgraph of the five-vertex path. In fact, the “if” implication holds for all k≥1. |
| Author | Chudnovsky, Maria Spirkl, Sophie Hajebi, Sepehr |
| Author_xml | – sequence: 1 givenname: Maria surname: Chudnovsky fullname: Chudnovsky, Maria organization: Princeton University – sequence: 2 givenname: Sepehr surname: Hajebi fullname: Hajebi, Sepehr email: shajebi@uwaterloo.ca organization: Department of Combinatorics and Optimization, University of Waterloo – sequence: 3 givenname: Sophie surname: Spirkl fullname: Spirkl, Sophie organization: Department of Combinatorics and Optimization, University of Waterloo |
| BookMark | eNp9kE1LAzEQhoNUsK3-AU8LnjxEJ5-bXIRSbCsUvOg5xDTRbdfNmmwP_nu3XUHwUOYwl_d5Z3gmaNTExiN0TeCOAJT3GYBrhoFyDEBAYnqGxoQzjaUmdITGQEFjLRW7QJOctwCgGBFjdLuucod3eB7rmKrmvVjhRfK-WCbbfuQixFTM6rrYPfBLdB5snf3V756i18Xjy3yF18_Lp_lsjR3jqsNK-ZKWwSrhlBVMcuZKGeQbt_1s3IZKT0FqIX0QoKX0XlLuoE8w7rwIbIpuht42xa-9z53Zxn1q-pOGEcIJo0KpPkWHlEsx5-SDaVP1adO3IWAOSsygxPRKzFGJoT2k_kGu6mxXxaZLtqpPo2xAc3vQ5NPfVyeoHzJzdDA |
| CitedBy_id | crossref_primary_10_1016_j_tcs_2025_115234 crossref_primary_10_1016_j_jcss_2025_103662 |
| Cites_doi | 10.1002/jgt.22028 10.1137/0210055 10.1137/21M1443352 10.1016/0196-6774(83)90032-9 10.1016/0304-3975(86)90184-2 10.1137/0202019 10.1007/s00453-013-9777-0 10.7551/mitpress/12274.003.0038 |
| ContentType | Journal Article |
| Copyright | The Author(s), under exclusive licence to János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| Copyright_xml | – notice: The Author(s), under exclusive licence to János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s00493-024-00106-2 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1439-6912 |
| EndPage | 1068 |
| ExternalDocumentID | 10_1007_s00493_024_00106_2 |
| GroupedDBID | -52 -5D -5G -BR -EM -ET -Y2 -~C -~X .86 .DC 06D 0R~ 0VY 199 1N0 1SB 2.D 203 28- 29F 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6J9 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAGAY AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACREN ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADYOE ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFYQB AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMTXH AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BBWZM BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ H~9 I09 IAO IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAS LLZTM M4Y MA- MQGED N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P9R PF- PKN PT4 PT5 QOK QOS R4E R89 R9I RHV RIG RNI RNS ROL RPX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW VH1 W23 W48 WIP WK8 YLTOR Z45 Z7X Z83 Z88 Z8R Z8W Z92 ZMTXR ZWQNP ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR CITATION |
| ID | FETCH-LOGICAL-c348t-88e727fa85c8a53643c76f6b4a4a4dcd26e206956ef50966ee624c0f6b34ce5f3 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001222563500002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0209-9683 |
| IngestDate | Thu Oct 02 16:35:55 EDT 2025 Sat Nov 29 06:43:09 EST 2025 Tue Nov 18 22:02:25 EST 2025 Fri Feb 21 02:40:17 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Keywords | Coloring Polynomial-time Algorithms List-Coloring Induced subgraphs |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c348t-88e727fa85c8a53643c76f6b4a4a4dcd26e206956ef50966ee624c0f6b34ce5f3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 3114132588 |
| PQPubID | 2043757 |
| PageCount | 6 |
| ParticipantIDs | proquest_journals_3114132588 crossref_primary_10_1007_s00493_024_00106_2 crossref_citationtrail_10_1007_s00493_024_00106_2 springer_journals_10_1007_s00493_024_00106_2 |
| PublicationCentury | 2000 |
| PublicationDate | 2024-10-01 |
| PublicationDateYYYYMMDD | 2024-10-01 |
| PublicationDate_xml | – month: 10 year: 2024 text: 2024-10-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Berlin/Heidelberg |
| PublicationPlace_xml | – name: Berlin/Heidelberg – name: Heidelberg |
| PublicationTitle | Combinatorica (Budapest. 1981) |
| PublicationTitleAbbrev | Combinatorica |
| PublicationYear | 2024 |
| Publisher | Springer Berlin Heidelberg Springer Nature B.V |
| Publisher_xml | – name: Springer Berlin Heidelberg – name: Springer Nature B.V |
| References | Holyer (CR5) 1981; 10 Couturier, Golovach, Kratsch, Paulusma (CR1) 2015; 71 Hajebi, Li, Spirkl (CR4) 2022; 36 Golovach, Johnson, Paulusma, Song (CR3) 2017; 84 Kamiński, Lozin (CR7) 2007; 2 Hopcroft, Karp (CR6) 1973; 2 CR8 Leven, Galil (CR9) 1983; 4 Edwards (CR2) 1986; 43 PA Golovach (106_CR3) 2017; 84 J-F Couturier (106_CR1) 2015; 71 S Hajebi (106_CR4) 2022; 36 JE Hopcroft (106_CR6) 1973; 2 M Kamiński (106_CR7) 2007; 2 D Leven (106_CR9) 1983; 4 I Holyer (106_CR5) 1981; 10 106_CR8 K Edwards (106_CR2) 1986; 43 |
| References_xml | – volume: 84 start-page: 331 issue: 4 year: 2017 end-page: 363 ident: CR3 article-title: A survey on the computational complexity of coloring graphs with forbidden subgraphs publication-title: J. Graph Theory doi: 10.1002/jgt.22028 – volume: 10 start-page: 718 issue: 4 year: 1981 end-page: 720 ident: CR5 article-title: The NP-completeness of edge-coloring publication-title: SIAM J. Comput. doi: 10.1137/0210055 – volume: 36 start-page: 2004 issue: 3 year: 2022 end-page: 2027 ident: CR4 article-title: Complexity dichotomy for list-5-coloring with a forbidden induced subgraph publication-title: SIAM J. Discrete Math. doi: 10.1137/21M1443352 – volume: 4 start-page: 35 issue: 1 year: 1983 end-page: 44 ident: CR9 article-title: NP completeness of finding the chromatic index of regular graphs publication-title: J. Algorithms doi: 10.1016/0196-6774(83)90032-9 – volume: 43 start-page: 337 issue: 2–3 year: 1986 end-page: 343 ident: CR2 article-title: The complexity of colouring problems on dense graphs publication-title: Theoret. Comput. Sci. doi: 10.1016/0304-3975(86)90184-2 – ident: CR8 – volume: 2 start-page: 225 year: 1973 end-page: 231 ident: CR6 article-title: An algorithm for maximum matchings in bipartite graphs publication-title: SIAM J. Comput. doi: 10.1137/0202019 – volume: 2 start-page: 61 issue: 1 year: 2007 end-page: 66 ident: CR7 article-title: Coloring edges and vertices of graphs without short or long cycles publication-title: Contrib. Discrete Math. – volume: 71 start-page: 21 issue: 1 year: 2015 end-page: 35 ident: CR1 article-title: List coloring in the absence of a linear forest publication-title: Algorithmica doi: 10.1007/s00453-013-9777-0 – volume: 36 start-page: 2004 issue: 3 year: 2022 ident: 106_CR4 publication-title: SIAM J. Discrete Math. doi: 10.1137/21M1443352 – volume: 43 start-page: 337 issue: 2–3 year: 1986 ident: 106_CR2 publication-title: Theoret. Comput. Sci. doi: 10.1016/0304-3975(86)90184-2 – volume: 10 start-page: 718 issue: 4 year: 1981 ident: 106_CR5 publication-title: SIAM J. Comput. doi: 10.1137/0210055 – ident: 106_CR8 doi: 10.7551/mitpress/12274.003.0038 – volume: 84 start-page: 331 issue: 4 year: 2017 ident: 106_CR3 publication-title: J. Graph Theory doi: 10.1002/jgt.22028 – volume: 71 start-page: 21 issue: 1 year: 2015 ident: 106_CR1 publication-title: Algorithmica doi: 10.1007/s00453-013-9777-0 – volume: 2 start-page: 61 issue: 1 year: 2007 ident: 106_CR7 publication-title: Contrib. Discrete Math. – volume: 4 start-page: 35 issue: 1 year: 1983 ident: 106_CR9 publication-title: J. Algorithms doi: 10.1016/0196-6774(83)90032-9 – volume: 2 start-page: 225 year: 1973 ident: 106_CR6 publication-title: SIAM J. Comput. doi: 10.1137/0202019 |
| SSID | ssj0008315 |
| Score | 2.3856895 |
| Snippet | Given an integer
k
>
4
and a graph
H
, we prove that, assuming P
≠
NP, the
List-
k
-Coloring Problem
restricted to
H
-free graphs can be solved in polynomial... Given an integer k>4 and a graph H, we prove that, assuming P≠NP, the List-k-Coloring Problem restricted to H-free graphs can be solved in polynomial time if... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1063 |
| SubjectTerms | Apexes Coloring Combinatorics Graph theory Graphs Mathematics Mathematics and Statistics Original Paper Polynomials |
| Title | List-k-Coloring H-Free Graphs for All k>4 |
| URI | https://link.springer.com/article/10.1007/s00493-024-00106-2 https://www.proquest.com/docview/3114132588 |
| Volume | 44 |
| WOSCitedRecordID | wos001222563500002&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: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1439-6912 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0008315 issn: 0209-9683 databaseCode: RSV dateStart: 19970301 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3dS8MwED9k-qAPfovTKX3wRTTQNWmWvghjOPcwh_jF3kqaXEA2Nlmnf79J1nYoKih97CWUu_Tud-TudwBnBmWS0SQmnGaKMKkpSTS3BtFIs1ZmQi09ZX6_NRiI4TC5K5rC8rLavbyS9J66anZzYNbdOTLiExliHe-qDXfCDWy4f3iu_K8o5hZEoeOeFLRolfl-j8_haIkxv1yL-mjT3frfd27DZoEug_biOOzACk52YeO2ombN9-C8bw1LRqQzXdTeBT3SnSEGN465Og8shg3a43EwumL78NS9fuz0SDEvgSjKxJwIgRaNGCliJWRMLdZQLW54xqR9tNIRxyjkNiFC40hfOCKPmAqtBGUKY0MPoDaZTvAQgtg0dZjR2KawTWawJdGZWnPmCMckwzo0S7WlqiATdzMtxmlFg-zVkFo1pF4NaVSHi2rN64JK41fpRmmNtPit8pTa7M2mz7EQdbgstb98_fNuR38TP4b1yBnQF-01oDafveEJrKn3-Us-O_XH7QOLmMq4 |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3dS8MwED9kCuqD3-J0ah98EQ10TZqmL8IYzonbEJ2yt9DmA2Rjk3X695tkbYeigtLHXkK5S-9-x939AnCmVRKnOA4RxalAJJEYxZIag0iF0yjVvkwcZX4n6vXYYBDf50NhWdHtXpQknacuh90smLU1R4JcIoOM410mJmJZxvyHx-fS_7L83oLAt9yTDOejMt_v8TkcLTDml7Koizatzf995xZs5OjSa8yPwzYsqfEOrHdLatZsF847xrBoiJqTee-d10atqVLejWWuzjyDYb3GaOQNr8gePLWu-802yu9LQAITNkOMKYNGdMJCwZIQG6whIqppShLzSCEDqgKfmoRIaUv6QpWiARG-kcBEqFDjfaiMJ2N1AF6o69JPcWhS2DrRKkqUNbWkxBKOJURVoV6ojYucTNzeaTHiJQ2yUwM3auBODTyowkW55nVOpfGrdK2wBs9_q4xjk72Z9DlkrAqXhfYXr3_e7fBv4qew2u53O7xz27s7grXAGtM18NWgMpu-qWNYEe-zl2x64o7eBxYxzZw |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dS8MwEA-iIvrgtzid2gdfRMO6Jk3TF2FM68Q5Bn6wt5DmA2SjG1v17zfp11RUEOljL6HcXZPfcXe_A-BUKx7GKPQhQbGAmEsEQ0mMQaRCcRBrV_KMMr8b9Hp0MAj7H7r4s2r3MiWZ9zRYlqYkbUykblSNbxbY2vwjhllQA80hvIRtIb2N1x-eq7OYFjMMPNfyUFJUtM18v8fnq2mON7-kSLObJ9r4_zdvgvUCdTqt3E22wIJKtsHafUXZOtsBZ11jcDiE7XFek-d0YDRVyrmxjNYzx2BbpzUaOcNLvAueouvHdgcWcxSgQJimkFJlUIrm1BeU-8hgEBEQTWLMzSOF9IjyXGICJaUtGQxRinhYuEYCYaF8jfbAYjJO1D5wfN2Ubox8E9o2sVYBV9YFJMGWiIxjVQPNUoVMFCTjdtbFiFX0yJkamFEDy9TAvBo4r9ZMcoqNX6XrpWVY8bvNGDJRnQmrfUpr4KK0xPz1z7sd_E38BKz0ryLWve3dHYJVz9oyq-urg8V0-qqOwLJ4S19m0-PMC98BDOPWgA |
| 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=List-k-Coloring+H-Free+Graphs+for+All+k%3E4&rft.jtitle=Combinatorica+%28Budapest.+1981%29&rft.au=Chudnovsky%2C+Maria&rft.au=Hajebi%2C+Sepehr&rft.au=Spirkl%2C+Sophie&rft.date=2024-10-01&rft.pub=Springer+Berlin+Heidelberg&rft.issn=0209-9683&rft.eissn=1439-6912&rft.volume=44&rft.issue=5&rft.spage=1063&rft.epage=1068&rft_id=info:doi/10.1007%2Fs00493-024-00106-2&rft.externalDocID=10_1007_s00493_024_00106_2 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0209-9683&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0209-9683&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0209-9683&client=summon |