Decremental optimization of vertex-colouring under the reconfiguration framework
Suppose that we are given a positive integer k, and a k-(vertex-)colouring of a given graph G. Then we are asked to find a colouring of G using the minimum number of colours among colourings that are reachable from by iteratively changing a colour assignment of exactly one vertex while maintaining t...
Uloženo v:
| Vydáno v: | International journal of computer mathematics. Computer systems theory Ročník 8; číslo 1; s. 80 - 92 |
|---|---|
| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Taylor & Francis
02.01.2023
|
| Témata: | |
| ISSN: | 2379-9927, 2379-9935 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Suppose that we are given a positive integer k, and a k-(vertex-)colouring
of a given graph G. Then we are asked to find a colouring of G using the minimum number of colours among colourings that are reachable from
by iteratively changing a colour assignment of exactly one vertex while maintaining the property of k-colourings. In this paper, we give linear-time algorithms to solve the problem for graphs of degeneracy at most two and for the case where
. These results imply linear-time algorithms for series-parallel graphs and grid graphs. In addition, we give linear-time algorithms for chordal graphs and cographs. On the other hand, we show that, for any
, this problem remains NP-hard for planar graphs with degeneracy three and maximum degree four. Thus, we obtain a complexity dichotomy for this problem with respect to the degeneracy of a graph and the number k of colours. |
|---|---|
| AbstractList | Suppose that we are given a positive integer k, and a k-(vertex-)colouring
of a given graph G. Then we are asked to find a colouring of G using the minimum number of colours among colourings that are reachable from
by iteratively changing a colour assignment of exactly one vertex while maintaining the property of k-colourings. In this paper, we give linear-time algorithms to solve the problem for graphs of degeneracy at most two and for the case where
. These results imply linear-time algorithms for series-parallel graphs and grid graphs. In addition, we give linear-time algorithms for chordal graphs and cographs. On the other hand, we show that, for any
, this problem remains NP-hard for planar graphs with degeneracy three and maximum degree four. Thus, we obtain a complexity dichotomy for this problem with respect to the degeneracy of a graph and the number k of colours. |
| Author | Tamura, Yuma Zhou, Xiao Suzuki, Akira Yanagisawa, Yusuke |
| Author_xml | – sequence: 1 givenname: Yusuke surname: Yanagisawa fullname: Yanagisawa, Yusuke email: yusuke.yanagisawa.r7@dc.tohoku.ac.jp organization: Tohoku University – sequence: 2 givenname: Akira surname: Suzuki fullname: Suzuki, Akira organization: Tohoku University – sequence: 3 givenname: Yuma surname: Tamura fullname: Tamura, Yuma organization: Tohoku University – sequence: 4 givenname: Xiao surname: Zhou fullname: Zhou, Xiao organization: Tohoku University |
| BookMark | eNp9kM1OwzAQhC1UJErpIyDlBVLWdhzHN1D5lSrBoXcrtdfFkNiVkwLl6UnVwpHTrFY7o53vnIxCDEjIJYUZhQquGJdKKSZnDBifMVoJUfATMt7vc6W4GP3NTJ6Rade9AQCVigMTY_JyiyZhi6Gvmyxuet_677r3MWTRZR-YevzKTWziNvmwzrbBYsr6V8wSmhicX2_T4dqlusXPmN4vyKmrmw6nR52Q5f3dcv6YL54fnuY3i9wwUfU54xaMo-Cq0jkG0hWlU7IqQVFpGFihChS0tEZYNCtEUJZJuyoHgQIpnxBxiDUpdl1CpzfJt3XaaQp6D0b_gtF7MPoIZvBdH3w-uJjaeni5sbqvd01MQ4dgfKf5_xE_yNpt7g |
| Cites_doi | 10.1002/jgt.22000 10.1007/978-3-030-48966-3_6 10.1016/0095-8956(79)90067-4 10.1016/j.jcss.2017.11.003 10.1006/jctb.1996.0030 10.1093/oxfordhb/9780190226992.013.32 10.1201/9780429280092-10 10.1007/s10878-020-00630-z 10.1007/978-3-319-13524-3_10 10.1016/j.disc.2007.07.028 10.1007/978-1-4684-2001-2_9 10.1137/0205021 10.1016/j.tcs.2009.08.023 10.1007/978-3-030-26176-4_26 10.1007/s10878-012-9490-y 10.1007/s00236-019-00336-8 10.1016/j.tcs.2010.12.005 10.1007/s00453-015-0009-7 10.1016/j.ejc.2017.10.010 10.1002/jgt.20514 10.3390/a11040052 |
| ContentType | Journal Article |
| Copyright | 2023 Informa UK Limited, trading as Taylor & Francis Group 2023 |
| Copyright_xml | – notice: 2023 Informa UK Limited, trading as Taylor & Francis Group 2023 |
| DBID | AAYXX CITATION |
| DOI | 10.1080/23799927.2023.2185543 |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISSN | 2379-9935 |
| EndPage | 92 |
| ExternalDocumentID | 10_1080_23799927_2023_2185543 2185543 |
| Genre | Research Article |
| GroupedDBID | 0BK 0R~ 30N AAGDL AAHIA AALDU AAMIU AAPUL AAQRR AASAQ ABCCY ABLIJ ABPAQ ABPEM ABXUL ABXYU ACGFS ADCVX ADFNY ADGTB AECIN AEEWU AEISY AFRVT AGDLA AHDZW AIJEM AIYEW AKBVH ALMA_UNASSIGNED_HOLDINGS ALQZU AQTUD BLEHA CCCUG DGEBU EBS EUPTU H13 KYCEM LJTGL M4Z O9- RIG RNANH ROSJB RTWRZ SOJIQ TASJS TBQAZ TDBHL TEJ TFL TFT TFW TTHFI TUROJ ZGOLN AAYXX CITATION |
| ID | FETCH-LOGICAL-c258t-23d0cf10f86ff207f46f97860917c20d594e516dc5decbee09d27db69d204e13 |
| IEDL.DBID | TFW |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000963708400005&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 2379-9927 |
| IngestDate | Sat Nov 29 06:13:30 EST 2025 Mon Oct 20 23:46:40 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c258t-23d0cf10f86ff207f46f97860917c20d594e516dc5decbee09d27db69d204e13 |
| PageCount | 13 |
| ParticipantIDs | informaworld_taylorfrancis_310_1080_23799927_2023_2185543 crossref_primary_10_1080_23799927_2023_2185543 |
| PublicationCentury | 2000 |
| PublicationDate | 2023-01-02 |
| PublicationDateYYYYMMDD | 2023-01-02 |
| PublicationDate_xml | – month: 01 year: 2023 text: 2023-01-02 day: 02 |
| PublicationDecade | 2020 |
| PublicationTitle | International journal of computer mathematics. Computer systems theory |
| PublicationYear | 2023 |
| Publisher | Taylor & Francis |
| Publisher_xml | – name: Taylor & Francis |
| References | Bonsma P.S. (CIT0004) 2009; 410 Feghali C. (CIT0011) 2016; 83 Bonamy M. (CIT0003) 2014; 27 Ito T. (CIT0015) 2011; 412 Markossian S.E. (CIT0020) 1996; 67 Ito T. (CIT0017) 2020; 43 Cereceda L. (CIT0008) 2011; 67 CIT0010 Cereceda L. (CIT0007) 2008; 308 CIT0001 CIT0023 CIT0022 Garey M.R. (CIT0012) 1979 Wrochna M. (CIT0024) 2018; 93 Johnson M. (CIT0018) 2016; 75 Bonsma P.S. (CIT0006) 2019; 56 Hatanaka T. (CIT0013) 2019; 102 Mynhardt C.M. (CIT0021) 2019 CIT0014 CIT0005 CIT0016 Bonamy M. (CIT0002) 2018; 69 CIT0009 CIT0019 |
| References_xml | – volume: 83 start-page: 340 issue: 4 year: 2016 ident: CIT0011 publication-title: J. Graph Theory doi: 10.1002/jgt.22000 – ident: CIT0001 doi: 10.1007/978-3-030-48966-3_6 – ident: CIT0009 doi: 10.1016/0095-8956(79)90067-4 – volume: 93 start-page: 1 year: 2018 ident: CIT0024 publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2017.11.003 – ident: CIT0014 – volume: 67 start-page: 1 issue: 1 year: 1996 ident: CIT0020 publication-title: J. Combin. Theory Ser. B doi: 10.1006/jctb.1996.0030 – ident: CIT0010 doi: 10.1093/oxfordhb/9780190226992.013.32 – start-page: 171 volume-title: 50 Years of Combinatorics, Graph Theory, and Computing year: 2019 ident: CIT0021 doi: 10.1201/9780429280092-10 – volume: 43 start-page: 1264 issue: 5 year: 2020 ident: CIT0017 publication-title: J. Comb. Optim. doi: 10.1007/s10878-020-00630-z – ident: CIT0005 doi: 10.1007/978-3-319-13524-3_10 – volume-title: Computers and Intractability: A Guide to the Theory of NP-Completeness year: 1979 ident: CIT0012 – volume: 308 start-page: 913 issue: 5 year: 2008 ident: CIT0007 publication-title: Discrete Math. doi: 10.1016/j.disc.2007.07.028 – ident: CIT0019 doi: 10.1007/978-1-4684-2001-2_9 – ident: CIT0023 doi: 10.1137/0205021 – volume: 410 start-page: 5215 issue: 50 year: 2009 ident: CIT0004 publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2009.08.023 – ident: CIT0016 doi: 10.1007/978-3-030-26176-4_26 – volume: 102 start-page: 423 issue: 3 year: 2019 ident: CIT0013 publication-title: IEICE Trans. Fundam. Electron. Commun. Comput. Sci. – volume: 27 start-page: 132 year: 2014 ident: CIT0003 publication-title: J. Comb. Optim. doi: 10.1007/s10878-012-9490-y – volume: 56 start-page: 619 year: 2019 ident: CIT0006 publication-title: Acta Inform. doi: 10.1007/s00236-019-00336-8 – volume: 412 start-page: 1054 issue: 12 year: 2011 ident: CIT0015 publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2010.12.005 – volume: 75 start-page: 295 year: 2016 ident: CIT0018 publication-title: Algorithmica doi: 10.1007/s00453-015-0009-7 – volume: 69 start-page: 200 year: 2018 ident: CIT0002 publication-title: Eur. J. Comb. doi: 10.1016/j.ejc.2017.10.010 – volume: 67 start-page: 69 issue: 1 year: 2011 ident: CIT0008 publication-title: J. Graph Theory doi: 10.1002/jgt.20514 – ident: CIT0022 doi: 10.3390/a11040052 |
| SSID | ssj0001793025 |
| Score | 2.2057483 |
| Snippet | Suppose that we are given a positive integer k, and a k-(vertex-)colouring
of a given graph G. Then we are asked to find a colouring of G using the minimum... |
| SourceID | crossref informaworld |
| SourceType | Index Database Publisher |
| StartPage | 80 |
| SubjectTerms | Combinatorial reconfiguration graph algorithms graph colouring linear-time algorithms |
| Title | Decremental optimization of vertex-colouring under the reconfiguration framework |
| URI | https://www.tandfonline.com/doi/abs/10.1080/23799927.2023.2185543 |
| Volume | 8 |
| WOSCitedRecordID | wos000963708400005&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: PRVAWR databaseName: Taylor & Francis Online customDbUrl: eissn: 2379-9935 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001793025 issn: 2379-9927 databaseCode: TFW dateStart: 20160102 isFulltext: true titleUrlDefault: https://www.tandfonline.com providerName: Taylor & Francis |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07T8MwELZQxcBCeYrykgdWF8dJ7GREQMVUdahEt6h-HOpAi9q04udzdhzRDrDAFGW4KDqffd9Zd99HyJ1RMgNZFkzKHFgmbMl0aQ0DK1SSq6k2AoLYhBoOi8mkHMVuwlVsq_Q1NDREEeGs9pt7qldtR9y9SBXCGqH6Xvq7jzkKU6Ln-8TU77fmePD6fcuC4ceD8qo3Yt6qHeP56UM7CWqHvnQr8Qy6__DLR-Qwok760ITJMdlz8xPSbRUdaNzgp2T05FFkw_dPF3iavMcxTboA6pWb3SfzNNdhtpH6-bMlRQRJQ1kNs7d1E08U2pavMzIePI8fX1jUXGBG5EXNRGq5gYRDIQEEV5BJwEJTIqxQRnCbl5nLE2lNbp3RzvESF9VqiQ-euSQ9J535Yu4uCEUslWJ1KdJsirBRZRpjRSTa8tSiK8D0SL_1c_XRMGtUSSQsbd1VeXdV0V09Um6vRlWHKw1o9Eeq9Ffbyz_YXpED_xruXcQ16dTLtbsh-2ZTz1bL2xBvX8pZ0xA |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV09T8MwED1BQYKFb0T59MDqktiJnYwIqIooFUMkukWN7UMdaFFJET8f20lEO8ACU4boouh89r07-d4DuFRSRCjShAoRI42YTmmRakVRMxnGclQohl5sQg4GyXCYLs7CuGuVrobGiijCn9Vuc7tmdHMl7opxaXENkx2n_d2xScrmRL4Ka7HNtY4_P-s-f_dZbAAGXnvVWVFn1gzy_PSlpRS1RGC6kHq62__x0zuwVQNPcl1Fyi6smMkebDeiDqTe4_vwdOuAZEX5T6b2QHmtJzXJFIkTbzaf1DFd-_FG4kbQZsSCSOIraxy_zKuQItjc-jqArHuX3fRoLbtAFYuTkjKuA4VhgIlAZIHESKCtNYVFFlKxQMdpZOJQaBVrowpjgtSuqy6EfQSRCfkhtCbTiTkCYuEUtwUm49HIIkcZFTZcWFjogGvrClRt6DSOzt8qco08rDlLG3flzl157a42pIvLkZe-q4GVBEnOf7U9_oPtBWz0ssd-3r8fPJzApnvl2zDsFFrlbG7OYF19lOP32bkPvi86ftc6 |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV09T8MwELWgIMRC-RTl0wOri2MndjIiSgUCVR0q0S1qbB_qQFu1KeLnYzuOaAdYYMoQXRSdn33vrLt7CN0oKWIQWUqESIDETGekyLQioJmMEjkqFAMvNiF7vXQ4zPqhmnARyipdDg3VoAh_VrvNPdNQV8TdMi4trWGy7aS_2zZG2ZDIN9GWpc7CgXzQff2-ZrH4o1561VkRZ1b38fz0pbUItTa_dCXydJv_8M_7aC_QTnxX4eQAbZjJIWrWkg447PAj1O84GlkN_MdTe5y8hz5NPAXspJvNJ3Fzrn1zI3YNaHNsKST2eTWM35YVoDDUNV_HaNB9GNw_kiC6QBRL0pIwrqmCiEIqABiVEAuwmaawvEIqRnWSxSaJhFaJNqowhmZ2VXUh7IPGJuInqDGZTswpwpZMcZteMh6PLG-UcWHBwqJCU66tK0C1ULv2cz6rRmvkUZhYWrsrd-7Kg7taKFtdjbz0dxpQCZDk_Ffbsz_YXqOdfqebvzz1ns_Rrnvj72DYBWqU86W5RNvqoxwv5lceel_Q79Xs |
| 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=Decremental+optimization+of+vertex-colouring+under+the+reconfiguration+framework&rft.jtitle=International+journal+of+computer+mathematics.+Computer+systems+theory&rft.au=Yanagisawa%2C+Yusuke&rft.au=Suzuki%2C+Akira&rft.au=Tamura%2C+Yuma&rft.au=Zhou%2C+Xiao&rft.date=2023-01-02&rft.pub=Taylor+%26+Francis&rft.issn=2379-9927&rft.eissn=2379-9935&rft.volume=8&rft.issue=1&rft.spage=80&rft.epage=92&rft_id=info:doi/10.1080%2F23799927.2023.2185543&rft.externalDocID=2185543 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2379-9927&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2379-9927&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2379-9927&client=summon |