{"id":"https://openalex.org/W1978379258","doi":"https://doi.org/10.1007/bf01215921","title":"On the minimal number of edges in color-critical graphs","display_name":"On the minimal number of edges in color-critical graphs","publication_year":1997,"publication_date":"1997-09-01","ids":{"openalex":"https://openalex.org/W1978379258","doi":"https://doi.org/10.1007/bf01215921","mag":"1978379258"},"language":"en","primary_location":{"id":"doi:10.1007/bf01215921","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01215921","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/A5008556299","display_name":"Michael Krivelevich","orcid":"https://orcid.org/0000-0003-2357-4982"},"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":true,"raw_author_name":"Michael Krivelevich","raw_affiliation_strings":["Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, 69978, Tel-Aviv, Israel","Department of Mathematics Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, 69978, Tel-Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Department of Mathematics Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008556299"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":3.0715,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.90287162,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"17","issue":"3","first_page":"401","last_page":"426"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9950000047683716,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9614999890327454,"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":0.8425089120864868},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8389624357223511},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49002134799957275},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.4631570875644684},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44998830556869507},{"id":"https://openalex.org/keywords/critical-graph","display_name":"Critical graph","score":0.4287009537220001},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.4197540879249573},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.14911901950836182},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.05090528726577759}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8425089120864868},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8389624357223511},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49002134799957275},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.4631570875644684},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44998830556869507},{"id":"https://openalex.org/C167750561","wikidata":"https://www.wikidata.org/wiki/Q1789512","display_name":"Critical graph","level":5,"score":0.4287009537220001},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.4197540879249573},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.14911901950836182},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.05090528726577759}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/bf01215921","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01215921","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:10.1.1.23.2800","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.23.2800","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tau.ac.il/~krivelev/14.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W36426682","https://openalex.org/W345637930","https://openalex.org/W1526777878","https://openalex.org/W1971849303","https://openalex.org/W1992504234","https://openalex.org/W1996680278","https://openalex.org/W2006544720","https://openalex.org/W2017899631","https://openalex.org/W2022925674","https://openalex.org/W2029971820","https://openalex.org/W2039034189","https://openalex.org/W2043731122","https://openalex.org/W2060664509","https://openalex.org/W2065634598","https://openalex.org/W2066843228","https://openalex.org/W2068871408","https://openalex.org/W2085716675","https://openalex.org/W2131309366","https://openalex.org/W2155360885","https://openalex.org/W2254576550","https://openalex.org/W2476848496","https://openalex.org/W2573541365","https://openalex.org/W2905110430","https://openalex.org/W4291439952"],"related_works":["https://openalex.org/W2562183448","https://openalex.org/W1984098916","https://openalex.org/W2046610653","https://openalex.org/W2168180506","https://openalex.org/W2091414672","https://openalex.org/W2891101917","https://openalex.org/W2951887113","https://openalex.org/W4390486240","https://openalex.org/W2049992750","https://openalex.org/W3178681420"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}