{"id":"https://openalex.org/W4243022563","doi":"https://doi.org/10.1002/(sici)1097-0118(199912)32:4<327::aid-jgt2>3.0.co;2-b","title":"Dirac's map-color theorem for choosability","display_name":"Dirac's map-color theorem for choosability","publication_year":1999,"publication_date":"1999-12-01","ids":{"openalex":"https://openalex.org/W4243022563","doi":"https://doi.org/10.1002/(sici)1097-0118(199912)32:4<327::aid-jgt2>3.0.co;2-b"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0118(199912)32:4<327::aid-jgt2>3.0.co;2-b","is_oa":true,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199912)32:4<327::aid-jgt2>3.0.co;2-b","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/%28SICI%291097-0118%28199912%2932%3A4%3C327%3A%3AAID-JGT2%3E3.0.CO%3B2-B","source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/%28SICI%291097-0118%28199912%2932%3A4%3C327%3A%3AAID-JGT2%3E3.0.CO%3B2-B","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016706643","display_name":"T. B\ufffdhme","orcid":null},"institutions":[{"id":"https://openalex.org/I119449181","display_name":"Technische Universit\u00e4t Ilmenau","ror":"https://ror.org/01weqhp73","country_code":"DE","type":"education","lineage":["https://openalex.org/I119449181"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"T. B\ufffdhme","raw_affiliation_strings":["Technical University of Ilmenau, D-98684 Ilmenau, Germany"],"affiliations":[{"raw_affiliation_string":"Technical University of Ilmenau, D-98684 Ilmenau, Germany","institution_ids":["https://openalex.org/I119449181"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005993212","display_name":"Bojan Mohar","orcid":"https://orcid.org/0000-0002-7408-6148"},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"B. Mohar","raw_affiliation_strings":["University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia"],"affiliations":[{"raw_affiliation_string":"University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia","institution_ids":["https://openalex.org/I153976015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069306005","display_name":"Michael Stiebitz","orcid":null},"institutions":[{"id":"https://openalex.org/I119449181","display_name":"Technische Universit\u00e4t Ilmenau","ror":"https://ror.org/01weqhp73","country_code":"DE","type":"education","lineage":["https://openalex.org/I119449181"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. Stiebitz","raw_affiliation_strings":["Technical University of Ilmenau, D-98684 Ilmenau, Germany"],"affiliations":[{"raw_affiliation_string":"Technical University of Ilmenau, D-98684 Ilmenau, Germany","institution_ids":["https://openalex.org/I119449181"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005993212"],"corresponding_institution_ids":["https://openalex.org/I153976015"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":1.7696,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.86170213,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"32","issue":"4","first_page":"327","last_page":"339"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994999766349792,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9958000183105469,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.989799976348877,"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/combinatorics","display_name":"Combinatorics","score":0.8311071991920471},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8201068639755249},{"id":"https://openalex.org/keywords/graph-minor","display_name":"Graph minor","score":0.5664242506027222},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5269875526428223},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.4246682822704315},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42120978236198425},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.25558871030807495},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.16659802198410034}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8311071991920471},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8201068639755249},{"id":"https://openalex.org/C140752511","wikidata":"https://www.wikidata.org/wiki/Q905837","display_name":"Graph minor","level":5,"score":0.5664242506027222},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5269875526428223},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.4246682822704315},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42120978236198425},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.25558871030807495},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.16659802198410034},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1097-0118(199912)32:4<327::aid-jgt2>3.0.co;2-b","is_oa":true,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199912)32:4<327::aid-jgt2>3.0.co;2-b","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/%28SICI%291097-0118%28199912%2932%3A4%3C327%3A%3AAID-JGT2%3E3.0.CO%3B2-B","source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1002/(sici)1097-0118(199912)32:4<327::aid-jgt2>3.0.co;2-b","is_oa":true,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199912)32:4<327::aid-jgt2>3.0.co;2-b","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/%28SICI%291097-0118%28199912%2932%3A4%3C327%3A%3AAID-JGT2%3E3.0.CO%3B2-B","source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4243022563.pdf"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1543445673","https://openalex.org/W1978313715","https://openalex.org/W1984670524","https://openalex.org/W1995650785","https://openalex.org/W2020422308","https://openalex.org/W2066843228","https://openalex.org/W2089023036","https://openalex.org/W2167282783","https://openalex.org/W2318115050","https://openalex.org/W2335170054","https://openalex.org/W3008084033","https://openalex.org/W4212970601"],"related_works":["https://openalex.org/W2022272459","https://openalex.org/W4287864711","https://openalex.org/W3183510330","https://openalex.org/W2179997638","https://openalex.org/W2057826895","https://openalex.org/W3103394879","https://openalex.org/W2972155844","https://openalex.org/W3216424522","https://openalex.org/W2525865568","https://openalex.org/W4251162746"],"abstract_inverted_index":{"It":[0],"is":[1,25],"proved":[2],"that":[3,32],"the":[4,28,33,42],"choice":[5],"number":[6,30],"of":[7,15],"every":[8],"graph":[9,44],"G":[10,40],"embedded":[11],"on":[12],"a":[13,47],"surface":[14],"Euler":[16],"genus":[17],"\u03b5":[18,22],"\u2265":[19],"1":[20],"and":[21,31,37],"\u2260":[23],"3":[24],"at":[26],"most":[27],"Heawood":[29],"equality":[34],"holds":[35],"if":[36,39],"only":[38],"contains":[41],"complete":[43],"KH(\u03b5)":[45],"as":[46],"subgraph.":[48],"\u00a9":[49],"1999":[50,61],"John":[51],"Wiley":[52],"&":[53],"Sons,":[54],"Inc.":[55],"J":[56],"Graph":[57],"Theory":[58],"32:":[59],"327\u2013339,":[60]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
