{"id":"https://openalex.org/W1968769959","doi":"https://doi.org/10.1016/0012-365x(92)90691-8","title":"The gap between the chromatic number of a graph and the rank of its adjacency matrix is superlinear","display_name":"The gap between the chromatic number of a graph and the rank of its adjacency matrix is superlinear","publication_year":1992,"publication_date":"1992-10-01","ids":{"openalex":"https://openalex.org/W1968769959","doi":"https://doi.org/10.1016/0012-365x(92)90691-8","mag":"1968769959"},"language":"en","primary_location":{"id":"doi:10.1016/0012-365x(92)90691-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(92)90691-8","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"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":"Discrete Mathematics","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/A5008113826","display_name":"Alexander Razborov","orcid":null},"institutions":[{"id":"https://openalex.org/I2801160905","display_name":"Steklov Mathematical Institute","ror":"https://ror.org/03zeg8w71","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2801160905","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"A.A. Razborov","raw_affiliation_strings":["Steklov Mathematical Institute, Vavilova, 42, GSP-1, 117966 Moscow, USSR"],"affiliations":[{"raw_affiliation_string":"Steklov Mathematical Institute, Vavilova, 42, GSP-1, 117966 Moscow, USSR","institution_ids":["https://openalex.org/I2801160905"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008113826"],"corresponding_institution_ids":["https://openalex.org/I2801160905"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":1.9187,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.84501445,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"108","issue":"1-3","first_page":"393","last_page":"396"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","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"}},"topics":[{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","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/T11476","display_name":"Graph theory and applications","score":0.9911999702453613,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9819999933242798,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8614969253540039},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8219897747039795},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.7362757921218872},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5973129272460938},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5083689093589783},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.49696972966194153},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4947220981121063},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4740300476551056},{"id":"https://openalex.org/keywords/wheel-graph","display_name":"Wheel graph","score":0.47246479988098145},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.20168006420135498},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.1350610852241516}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8614969253540039},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8219897747039795},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.7362757921218872},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5973129272460938},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5083689093589783},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.49696972966194153},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4947220981121063},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4740300476551056},{"id":"https://openalex.org/C148364342","wikidata":"https://www.wikidata.org/wiki/Q948887","display_name":"Wheel graph","level":5,"score":0.47246479988098145},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.20168006420135498},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.1350610852241516}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0012-365x(92)90691-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(92)90691-8","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"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":"Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1551614270","https://openalex.org/W1978387065","https://openalex.org/W1998270481","https://openalex.org/W2057661677","https://openalex.org/W2145501841","https://openalex.org/W2983896310","https://openalex.org/W6650135113"],"related_works":["https://openalex.org/W4213150077","https://openalex.org/W2369410163","https://openalex.org/W2982430984","https://openalex.org/W2078477160","https://openalex.org/W2059018062","https://openalex.org/W2604585036","https://openalex.org/W1991172810","https://openalex.org/W125803343","https://openalex.org/W1989103179","https://openalex.org/W2117632582"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}