{"id":"https://openalex.org/W2022119896","doi":"https://doi.org/10.1007/bf01361706","title":"\ufffdber einen Satz von K. Wagner zum Vierfarbenproblem","display_name":"\ufffdber einen Satz von K. Wagner zum Vierfarbenproblem","publication_year":1964,"publication_date":"1964-02-01","ids":{"openalex":"https://openalex.org/W2022119896","doi":"https://doi.org/10.1007/bf01361706","mag":"2022119896"},"language":"de","primary_location":{"id":"doi:10.1007/bf01361706","doi":"https://doi.org/10.1007/bf01361706","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01361706","pdf_url":null,"source":{"id":"https://openalex.org/S192217950","display_name":"Mathematische Annalen","issn_l":"0025-5831","issn":["0025-5831","1432-1807"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematische Annalen","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088098295","display_name":"Rudolf Halin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"R. Halin","raw_affiliation_strings":["K\u00f6ln"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"K\u00f6ln","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5088098295"],"corresponding_institution_ids":[],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":null,"fwci":2.4373,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.88758782,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"153","issue":"1","first_page":"47","last_page":"62"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9570000171661377,"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":0.9570000171661377,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.010499999858438969,"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":0.005200000014156103,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/four-color-problem","display_name":"four-color problem","score":0.7940000295639038},{"id":"https://openalex.org/keywords/four-color-theorem","display_name":"four-color theorem","score":0.5910000205039978},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"graph coloring","score":0.6990000009536743},{"id":"https://openalex.org/keywords/planar-graphs","display_name":"planar graphs","score":0.9110000133514404}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7803991436958313},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.47698479890823364},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.20551550388336182}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01361706","doi":"https://doi.org/10.1007/bf01361706","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01361706","pdf_url":null,"source":{"id":"https://openalex.org/S192217950","display_name":"Mathematische Annalen","issn_l":"0025-5831","issn":["0025-5831","1432-1807"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematische Annalen","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1984155042","https://openalex.org/W1992457909","https://openalex.org/W2022942352","https://openalex.org/W2055691900","https://openalex.org/W2071321409","https://openalex.org/W2321253933","https://openalex.org/W7082487165"],"related_works":["https://openalex.org/W2772465410","https://openalex.org/W2577618728","https://openalex.org/W2318498127","https://openalex.org/W575055273","https://openalex.org/W2978509545","https://openalex.org/W2320452564","https://openalex.org/W2480281002","https://openalex.org/W1974528683","https://openalex.org/W2014581752","https://openalex.org/W2331703606"],"abstract_inverted_index":null,"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-09-22T06:50:58.402377","created_date":"2016-06-24T00:00:00"}