{"id":"https://openalex.org/W2021328395","doi":"https://doi.org/10.1007/s004930070005","title":"On the Number of Edges in Colour-Critical Graphs and Hypergraphs","display_name":"On the Number of Edges in Colour-Critical Graphs and Hypergraphs","publication_year":2000,"publication_date":"2000-04-01","ids":{"openalex":"https://openalex.org/W2021328395","doi":"https://doi.org/10.1007/s004930070005","mag":"2021328395"},"language":"en","primary_location":{"id":"doi:10.1007/s004930070005","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s004930070005","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","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/A5080894223","display_name":"Alexandr Kostochka","orcid":"https://orcid.org/0000-0002-6363-3804"},"institutions":[{"id":"https://openalex.org/I183874917","display_name":"Urbana University","ror":"https://ror.org/04kp3hw27","country_code":"US","type":"education","lineage":["https://openalex.org/I183874917"]},{"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/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]},{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]}],"countries":["BG","CZ","US"],"is_corresponding":true,"raw_author_name":"A. V. Kostochka","raw_affiliation_strings":["Institute of Mathematics; 630090 Novosibirsk, Russia;  and  University of Illinois at Urbana-Chamaign; Urbana, IL61801, USA;","Institute of Mathematics","Urbana, IL61801, USA","630090 Novosibirsk, Russia","University of Illinois at Urbana-Chamaign"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics; 630090 Novosibirsk, Russia;  and  University of Illinois at Urbana-Chamaign; Urbana, IL61801, USA;","institution_ids":["https://openalex.org/I157725225","https://openalex.org/I183874917"]},{"raw_affiliation_string":"Institute of Mathematics","institution_ids":["https://openalex.org/I4210105926","https://openalex.org/I4210120266"]},{"raw_affiliation_string":"Urbana, IL61801, USA","institution_ids":["https://openalex.org/I183874917"]},{"raw_affiliation_string":"630090 Novosibirsk, Russia","institution_ids":[]},{"raw_affiliation_string":"University of Illinois at Urbana-Chamaign","institution_ids":["https://openalex.org/I157725225"]}]},{"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":["Ilmenau Technical University; 98684 Ilmenau, Germany;","Ilmenau Technical University","98684 Ilmenau, Germany"],"affiliations":[{"raw_affiliation_string":"Ilmenau Technical University; 98684 Ilmenau, Germany;","institution_ids":["https://openalex.org/I119449181"]},{"raw_affiliation_string":"Ilmenau Technical University","institution_ids":["https://openalex.org/I119449181"]},{"raw_affiliation_string":"98684 Ilmenau, Germany","institution_ids":["https://openalex.org/I119449181"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080894223"],"corresponding_institution_ids":["https://openalex.org/I157725225","https://openalex.org/I183874917","https://openalex.org/I4210105926","https://openalex.org/I4210120266"],"apc_list":null,"apc_paid":null,"fwci":3.9851,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.93933709,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"20","issue":"4","first_page":"521","last_page":"530"},"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":0.9991999864578247,"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":0.9991999864578247,"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":0.9911999702453613,"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":0.9889000058174133,"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":0.8772603273391724},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8448795080184937},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.792604923248291},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5462299585342407},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5106731057167053},{"id":"https://openalex.org/keywords/critical-graph","display_name":"Critical graph","score":0.4281831979751587},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4247973561286926},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.2341943383216858},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.19362667202949524}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8772603273391724},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8448795080184937},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.792604923248291},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5462299585342407},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5106731057167053},{"id":"https://openalex.org/C167750561","wikidata":"https://www.wikidata.org/wiki/Q1789512","display_name":"Critical graph","level":5,"score":0.4281831979751587},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4247973561286926},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.2341943383216858},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.19362667202949524}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s004930070005","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s004930070005","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.300.3039","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.300.3039","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uiuc.edu/~kostochk/docs/2000/jctb2000Sti.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1978379258","https://openalex.org/W2009629999","https://openalex.org/W2025484786","https://openalex.org/W2068871408","https://openalex.org/W2071305757","https://openalex.org/W2167282783","https://openalex.org/W2766289302"],"related_works":["https://openalex.org/W1524556636","https://openalex.org/W1988533413","https://openalex.org/W3127534791","https://openalex.org/W2562183448","https://openalex.org/W1984098916","https://openalex.org/W2046610653","https://openalex.org/W2168180506","https://openalex.org/W2057367302","https://openalex.org/W2091414672","https://openalex.org/W3178681420"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}