{"id":"https://openalex.org/W4241626594","doi":"https://doi.org/10.1007/s00454-009-9171-5","title":"Polychromatic Colorings of Plane Graphs","display_name":"Polychromatic Colorings of Plane Graphs","publication_year":2009,"publication_date":"2009-06-29","ids":{"openalex":"https://openalex.org/W4241626594","doi":"https://doi.org/10.1007/s00454-009-9171-5"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-009-9171-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-009-9171-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-009-9171-5.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-009-9171-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083469386","display_name":"Noga Alon","orcid":"https://orcid.org/0000-0003-1332-4883"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Noga Alon","raw_affiliation_strings":["Tel Aviv University, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008662509","display_name":"Robert Berke","orcid":null},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Robert Berke","raw_affiliation_strings":["Tokyo Institute of Technology, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Tokyo Institute of Technology, Tokyo, Japan","institution_ids":["https://openalex.org/I114531698"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077490455","display_name":"Kevin Buchin","orcid":"https://orcid.org/0000-0002-3022-7877"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Kevin Buchin","raw_affiliation_strings":["Universiteit Utrecht, Utrecht, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Universiteit Utrecht, Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086805770","display_name":"Maike Buchin","orcid":"https://orcid.org/0000-0002-3446-4343"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Maike Buchin","raw_affiliation_strings":["Universiteit Utrecht, Utrecht, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Universiteit Utrecht, Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013632751","display_name":"P\u00e9ter Csorba","orcid":null},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"P\u00e9ter Csorba","raw_affiliation_strings":["TU Eindhoven, Eindhoven, The Netherlands"],"affiliations":[{"raw_affiliation_string":"TU Eindhoven, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015757567","display_name":"Saswata Shannigrahi","orcid":null},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Saswata Shannigrahi","raw_affiliation_strings":["Tata Inst. of Fund. Research, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Tata Inst. of Fund. Research, Mumbai, India","institution_ids":["https://openalex.org/I11947397"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000420564","display_name":"Bettina Speckmann","orcid":"https://orcid.org/0000-0002-8514-7858"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Bettina Speckmann","raw_affiliation_strings":["TU Eindhoven, Eindhoven, The Netherlands"],"affiliations":[{"raw_affiliation_string":"TU Eindhoven, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030467731","display_name":"Philipp Zumstein","orcid":"https://orcid.org/0000-0002-6485-9434"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Philipp Zumstein","raw_affiliation_strings":["ETH Z\u00fcrich, Z\u00fcrich, Switzerland"],"affiliations":[{"raw_affiliation_string":"ETH Z\u00fcrich, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5008662509"],"corresponding_institution_ids":["https://openalex.org/I114531698"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.0602,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.79787193,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"42","issue":"3","first_page":"421","last_page":"442"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9872999787330627,"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":0.9872999787330627,"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":0.9668999910354614,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9329000115394592,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8936665058135986},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7731590270996094},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6256934404373169},{"id":"https://openalex.org/keywords/complete-coloring","display_name":"Complete coloring","score":0.5582877397537231},{"id":"https://openalex.org/keywords/fractional-coloring","display_name":"Fractional coloring","score":0.5427688360214233},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4870920181274414},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4483437240123749},{"id":"https://openalex.org/keywords/colored","display_name":"Colored","score":0.4287665784358978},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38167139887809753},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.23479145765304565},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.096642404794693},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06768804788589478}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8936665058135986},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7731590270996094},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6256934404373169},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.5582877397537231},{"id":"https://openalex.org/C158319403","wikidata":"https://www.wikidata.org/wiki/Q5477527","display_name":"Fractional coloring","level":5,"score":0.5427688360214233},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4870920181274414},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4483437240123749},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.4287665784358978},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38167139887809753},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.23479145765304565},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.096642404794693},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06768804788589478},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00454-009-9171-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-009-9171-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-009-9171-5.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/983d08b6-4313-4a29-b7a8-3c2f064940fa","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/983d08b6-4313-4a29-b7a8-3c2f064940fa","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Alon, N, Berke, R, Buchin, K, Buchin, M, Csorba, P, Shannigrahi, S, Speckmann, B & Zumstein, P 2009, 'Polychromatic colorings of plane graphs', Discrete and Computational Geometry, vol. 42, no. 3, pp. 421-442. https://doi.org/10.1007/s00454-009-9171-5","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:tue:oai:pure.tue.nl:publications/983d08b6-4313-4a29-b7a8-3c2f064940fa","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/983d08b6-4313-4a29-b7a8-3c2f064940fa","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete and Computational Geometry, 42(3), 421 - 442. Springer","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00454-009-9171-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-009-9171-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-009-9171-5.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6100000143051147}],"awards":[{"id":"https://openalex.org/G258765838","display_name":null,"funder_award_id":"639.022.707","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G3119829495","display_name":null,"funder_award_id":"642.065.503","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"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320322596","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4241626594.pdf","grobid_xml":"https://content.openalex.org/works/W4241626594.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1528987669","https://openalex.org/W1531267818","https://openalex.org/W1554387854","https://openalex.org/W1974811277","https://openalex.org/W1981455469","https://openalex.org/W2019145424","https://openalex.org/W2025961184","https://openalex.org/W2045611333","https://openalex.org/W2059233598","https://openalex.org/W2061541114","https://openalex.org/W2071826698","https://openalex.org/W2086039438","https://openalex.org/W2116854100","https://openalex.org/W2133839024","https://openalex.org/W2288132780","https://openalex.org/W2333732752","https://openalex.org/W3004234532","https://openalex.org/W4246652748"],"related_works":["https://openalex.org/W4311345810","https://openalex.org/W4385455827","https://openalex.org/W2375099373","https://openalex.org/W2376754815","https://openalex.org/W4236195035","https://openalex.org/W2793500002","https://openalex.org/W151506147","https://openalex.org/W2385428710","https://openalex.org/W1527284691","https://openalex.org/W2359963263"],"abstract_inverted_index":{"We":[0,67,105],"show":[1,69],"that":[2,27,54,70],"the":[3,71,144,153],"vertices":[4,19,52],"of":[5,59,73,126,135,138],"any":[6],"plane":[7,41,77],"graph":[8,78],"in":[9,31,86,91,95,149],"which":[10,87,116,143],"every":[11,28,32,92],"face":[12,93,118],"is":[13,35,94,100,148,156],"incident":[14,47],"to":[15,48,113],"at":[16,49],"least":[17,50],"g":[18,51],"can":[20],"be":[21],"colored":[22],"by":[23,83],"\u230a(3g\u22125)/4\u230b":[24],"colors":[25,85,89],"so":[26],"color":[29],"appears":[30],"face.":[33],"This":[34],"nearly":[36],"tight,":[37],"as":[38],"there":[39],"are":[40,46],"graphs":[42,115],"where":[43],"all":[44,88],"faces":[45],"and":[53,99,151],"admit":[55],"no":[56],"vertex":[57,81],"coloring":[58,82],"this":[60,107],"type":[61],"with":[62],"more":[63],"than":[64],"\u230a(3g+1)/4\u230b":[65],"colors.":[66],"further":[68],"problem":[72,147],"determining":[74],"whether":[75],"a":[76,80,121],"admits":[79],"k":[84],"appear":[90],"\u2118":[96],"for":[97,103,109,142,152],"k=2":[98],"$\\mathcal{NP}$":[101,157],"-complete":[102],"k=3,4.":[104],"refine":[106],"result":[108],"polychromatic":[110],"3-colorings":[111],"restricted":[112],"2-connected":[114],"have":[117],"sizes":[119],"from":[120],"prescribed":[122],"(possibly":[123],"infinite)":[124],"set":[125],"integers.":[127],"Thereby":[128],"we":[129],"find":[130],"an":[131],"almost":[132],"complete":[133],"characterization":[134],"these":[136],"sets":[137],"integers":[139],"(face":[140],"sizes)":[141],"corresponding":[145],"decision":[146],"\u2118,":[150],"others":[154],"it":[155],"-complete.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}