{"id":"https://openalex.org/W4225614383","doi":"https://doi.org/10.1016/j.jctb.2022.03.004","title":"A simple proof of the Map Color Theorem for nonorientable surfaces","display_name":"A simple proof of the Map Color Theorem for nonorientable surfaces","publication_year":2022,"publication_date":"2022-04-06","ids":{"openalex":"https://openalex.org/W4225614383","doi":"https://doi.org/10.1016/j.jctb.2022.03.004"},"language":"en","primary_location":{"id":"doi:10.1016/j.jctb.2022.03.004","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jctb.2022.03.004","pdf_url":null,"source":{"id":"https://openalex.org/S2939117604","display_name":"Journal of Combinatorial Theory Series B","issn_l":"0095-8956","issn":["0095-8956","1096-0902"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Theory, Series B","raw_type":"journal-article"},"type":"article","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/A5022008470","display_name":"Vladimir P. Korzhik","orcid":"https://orcid.org/0000-0001-8685-5648"},"institutions":[{"id":"https://openalex.org/I4210145787","display_name":"Pidstryhach Institute for Applied Problems of Mechanics and Mathematics","ror":"https://ror.org/05dry3213","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I4210145787"]},{"id":"https://openalex.org/I149851306","display_name":"National Academy of Sciences of Ukraine","ror":"https://ror.org/00je4t102","country_code":"UA","type":"funder","lineage":["https://openalex.org/I149851306"]}],"countries":["UA"],"is_corresponding":true,"raw_author_name":"Vladimir P. Korzhik","raw_affiliation_strings":["Pidstryhach Institute for Applied Problems in Mechanics and Mathematics of National Academy of Sciences of Ukraine, Lviv, Ukraine"],"affiliations":[{"raw_affiliation_string":"Pidstryhach Institute for Applied Problems in Mechanics and Mathematics of National Academy of Sciences of Ukraine, Lviv, Ukraine","institution_ids":["https://openalex.org/I4210145787","https://openalex.org/I149851306"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022008470"],"corresponding_institution_ids":["https://openalex.org/I149851306","https://openalex.org/I4210145787"],"apc_list":{"value":3420,"currency":"USD","value_usd":3420},"apc_paid":null,"fwci":0.3995,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55286281,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"156","issue":null,"first_page":"1","last_page":"17"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9925000071525574,"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"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9925000071525574,"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"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.987500011920929,"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/embedding","display_name":"Embedding","score":0.9108037948608398},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7745082378387451},{"id":"https://openalex.org/keywords/graph-embedding","display_name":"Graph embedding","score":0.5090014934539795},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5001637935638428},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4989309310913086},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4871211051940918},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34910398721694946},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3384968638420105},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12066498398780823},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.059927552938461304}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.9108037948608398},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7745082378387451},{"id":"https://openalex.org/C75564084","wikidata":"https://www.wikidata.org/wiki/Q5597085","display_name":"Graph embedding","level":3,"score":0.5090014934539795},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5001637935638428},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4989309310913086},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4871211051940918},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34910398721694946},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3384968638420105},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12066498398780823},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.059927552938461304},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.jctb.2022.03.004","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jctb.2022.03.004","pdf_url":null,"source":{"id":"https://openalex.org/S2939117604","display_name":"Journal of Combinatorial Theory Series B","issn_l":"0095-8956","issn":["0095-8956","1096-0902"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Theory, Series B","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W586151124","https://openalex.org/W1558273801","https://openalex.org/W1907007920","https://openalex.org/W1974974857","https://openalex.org/W1987602560","https://openalex.org/W1996246805","https://openalex.org/W2000375873","https://openalex.org/W2007612053","https://openalex.org/W2034485257","https://openalex.org/W2036085221","https://openalex.org/W2078554428","https://openalex.org/W2084615189","https://openalex.org/W2133378485","https://openalex.org/W3008084033","https://openalex.org/W4239288018","https://openalex.org/W6679906374"],"related_works":["https://openalex.org/W3036264823","https://openalex.org/W3206528106","https://openalex.org/W2123605750","https://openalex.org/W2912814903","https://openalex.org/W2088740331","https://openalex.org/W2950907416","https://openalex.org/W3038102983","https://openalex.org/W2082479932","https://openalex.org/W2932872266","https://openalex.org/W4281484020"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
