{"id":"https://openalex.org/W277046565","doi":"https://doi.org/10.37236/6303","title":"Extension from Precoloured Sets of Edges","display_name":"Extension from Precoloured Sets of Edges","publication_year":2018,"publication_date":"2018-07-13","ids":{"openalex":"https://openalex.org/W277046565","doi":"https://doi.org/10.37236/6303","mag":"277046565"},"language":"en","primary_location":{"id":"doi:10.37236/6303","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6303","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/6303","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006310630","display_name":"Katherine Edwards","orcid":"https://orcid.org/0000-0002-7931-7312"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Katherine Edwards","raw_affiliation_strings":["Nokia Bell Labs","Department of Computer Science (Princeton University 35 Olden Street, Princeton, NJ 08540-5233 - United States)"],"affiliations":[{"raw_affiliation_string":"Nokia Bell Labs","institution_ids":[]},{"raw_affiliation_string":"Department of Computer Science (Princeton University 35 Olden Street, Princeton, NJ 08540-5233 - United States)","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070979870","display_name":"Ant\u00f3nio Gir\u00e3o","orcid":"https://orcid.org/0000-0003-3065-6636"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210096386","display_name":"Bridge University","ror":"https://ror.org/00cbm0437","country_code":"SS","type":"education","lineage":["https://openalex.org/I4210096386"]}],"countries":["GB","SS"],"is_corresponding":false,"raw_author_name":"Ant\u00f3nio Gir\u00e3o","raw_affiliation_strings":["Cambridge University","DPMMS - Department of Pure Mathematics and Mathematical Statistics (Wilberforce Road, GB - Cambridge CB3 0WB - United Kingdom)"],"affiliations":[{"raw_affiliation_string":"Cambridge University","institution_ids":["https://openalex.org/I4210096386","https://openalex.org/I241749"]},{"raw_affiliation_string":"DPMMS - Department of Pure Mathematics and Mathematical Statistics (Wilberforce Road, GB - Cambridge CB3 0WB - United Kingdom)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018271059","display_name":"Jan van den Heuvel","orcid":"https://orcid.org/0000-0003-0897-9148"},"institutions":[{"id":"https://openalex.org/I909854389","display_name":"London School of Economics and Political Science","ror":"https://ror.org/0090zs177","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I909854389"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jan Van den Heuvel","raw_affiliation_strings":["London School of Economics","LSE - Department Mathematics [London] (Columbia House London School of Economics Houghton Street London WC2A 2AE, UK - United Kingdom)"],"affiliations":[{"raw_affiliation_string":"London School of Economics","institution_ids":["https://openalex.org/I909854389"]},{"raw_affiliation_string":"LSE - Department Mathematics [London] (Columbia House London School of Economics Houghton Street London WC2A 2AE, UK - United Kingdom)","institution_ids":["https://openalex.org/I909854389"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019911064","display_name":"Ross J. Kang","orcid":"https://orcid.org/0000-0002-4219-593X"},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Ross J. Kang","raw_affiliation_strings":["Radboud University Nijmegen","IMAPP - Applied Stochastics (Netherlands)"],"affiliations":[{"raw_affiliation_string":"Radboud University Nijmegen","institution_ids":["https://openalex.org/I145872427"]},{"raw_affiliation_string":"IMAPP - Applied Stochastics (Netherlands)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031977700","display_name":"Gregory J. Puleo","orcid":"https://orcid.org/0000-0002-0502-981X"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I82497590","display_name":"Auburn University","ror":"https://ror.org/02v80fc35","country_code":"US","type":"education","lineage":["https://openalex.org/I82497590"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gregory J. Puleo","raw_affiliation_strings":["Auburn University","CSL - Coordinated Science Laboratory (University of Illinois at Urbana-Champaign 1308 W Main Street Urbana, IL 61801-2307 - United States)"],"affiliations":[{"raw_affiliation_string":"Auburn University","institution_ids":["https://openalex.org/I82497590"]},{"raw_affiliation_string":"CSL - Coordinated Science Laboratory (University of Illinois at Urbana-Champaign 1308 W Main Street Urbana, IL 61801-2307 - United States)","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014744746","display_name":"Jean\u2010S\u00e9bastien Sereni","orcid":null},"institutions":[{"id":"https://openalex.org/I4210100283","display_name":"Laboratoire des Sciences de l'Ing\u00e9nieur, de l'Informatique et de l'Imagerie","ror":"https://ror.org/00k4e5n71","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I2801509770","https://openalex.org/I4210095849","https://openalex.org/I4210100283","https://openalex.org/I4210159245","https://openalex.org/I68947357"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-S\u00e9bastien Sereni","raw_affiliation_strings":["CNRS, CSTB (ICube)","ORPAILLEUR - Knowledge  representation, reasonning (France)"],"affiliations":[{"raw_affiliation_string":"CNRS, CSTB (ICube)","institution_ids":["https://openalex.org/I4210100283"]},{"raw_affiliation_string":"ORPAILLEUR - Knowledge  representation, reasonning (France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5006310630"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00127246,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"25","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9817000031471252,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9451000094413757,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.8589228987693787},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4755920171737671},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35150498151779175},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1583440601825714}],"concepts":[{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.8589228987693787},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4755920171737671},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35150498151779175},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1583440601825714}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.37236/6303","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6303","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:eprints.lse.ac.uk:90166","is_oa":true,"landing_page_url":"https://orcid.org/0000-0003-0897-9148>,","pdf_url":"http://eprints.lse.ac.uk/90166/1/van%20den%20Heuvel_Extension%20precoloured%20sets_2018.pdf","source":{"id":"https://openalex.org/S4306401593","display_name":"London School of Economics and Political Science Research Online (London School of Economics and Political Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I909854389","host_organization_name":"London School of Economics and Political Science","host_organization_lineage":["https://openalex.org/I909854389"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:arXiv.org:1407.4339","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1407.4339","pdf_url":"https://arxiv.org/pdf/1407.4339","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.764.5488","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.764.5488","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1407.4339.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01024843v2","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-01024843","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.archives-ouvertes.fr/hal-01024843","raw_type":"\\ninfo:eu-repo/semantics/report\\n"},{"id":"pmh:oai:HAL:hal-01024843v3","is_oa":false,"landing_page_url":"https://hal.science/hal-01024843","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The Electronic Journal of Combinatorics, 2018, ⟨10.37236/6303⟩","raw_type":"Journal articles"},{"id":"pmh:oai:repository.ubn.ru.nl:2066/194141","is_oa":false,"landing_page_url":"http://hdl.handle.net/2066/194141","pdf_url":null,"source":{"id":"https://openalex.org/S4306401067","display_name":"Radboud Repository (Radboud University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145872427","host_organization_name":"Radboud University Nijmegen","host_organization_lineage":["https://openalex.org/I145872427"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The Electronic Journal of Combinatorics, 25, 3, pp. 1-28","raw_type":"Article / Letter to editor"},{"id":"doi:10.48550/arxiv.1407.4339","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1407.4339","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/6303","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6303","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G405619435","display_name":null,"funder_award_id":"639.031.138","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G629491556","display_name":null,"funder_award_id":"(NWO)","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G8688676036","display_name":null,"funder_award_id":"639.032.614","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W3297276","https://openalex.org/W655585282","https://openalex.org/W1574175535","https://openalex.org/W1614675393","https://openalex.org/W1985316243","https://openalex.org/W1995705069","https://openalex.org/W2013202788","https://openalex.org/W2014385271","https://openalex.org/W2022269624","https://openalex.org/W2024769658","https://openalex.org/W2025328375","https://openalex.org/W2025536143","https://openalex.org/W2026087461","https://openalex.org/W2044004462","https://openalex.org/W2046229563","https://openalex.org/W2057809218","https://openalex.org/W2063149200","https://openalex.org/W2069867486","https://openalex.org/W2088148599","https://openalex.org/W2089023036","https://openalex.org/W2103223314","https://openalex.org/W2130898844","https://openalex.org/W2155893902","https://openalex.org/W2330003519","https://openalex.org/W2998904250","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694"],"abstract_inverted_index":{"We":[0,37],"consider":[1],"precolouring":[2],"extension":[3],"problems":[4],"for":[5],"proper":[6],"edge-colourings":[7],"of":[8,19,28,32,57,60,80],"graphs":[9],"and":[10,21,76],"multigraphs,":[11],"in":[12,30,41],"an":[13],"attempt":[14],"to":[15,49,54,67,70],"prove":[16],"stronger":[17],"versions":[18],"Vizing's":[20],"Shannon's":[22],"bounds":[23],"on":[24],"the":[25,42,71],"chromatic":[26],"index":[27],"(multi)graphs":[29],"terms":[31],"their":[33],"maximum":[34],"degree":[35],"$\\Delta$.":[36],"are":[38],"especially":[39],"interested":[40],"following":[43],"question:":[44],"when":[45],"is":[46],"it":[47],"possible":[48],"extend":[50],"a":[51,55,61],"precoloured":[52],"matching":[53],"colouring":[56],"all":[58],"edges":[59],"(multi)graph?":[62],"This":[63],"question":[64],"turns":[65],"out":[66],"be":[68],"related":[69],"notorious":[72],"List":[73],"Colouring":[74],"Conjecture":[75],"other":[77],"classic":[78],"notions":[79],"choosability.":[81]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}