{"id":"https://openalex.org/W1972004553","doi":"https://doi.org/10.1002/(sici)1097-0118(199709)26:1<1::aid-jgt1>3.0.co;2-n","title":"Rank and chromatic number of a graph","display_name":"Rank and chromatic number of a graph","publication_year":1997,"publication_date":"1997-09-01","ids":{"openalex":"https://openalex.org/W1972004553","doi":"https://doi.org/10.1002/(sici)1097-0118(199709)26:1<1::aid-jgt1>3.0.co;2-n","mag":"1972004553"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0118(199709)26:1<1::aid-jgt1>3.0.co;2-n","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199709)26:1<1::aid-jgt1>3.0.co;2-n","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","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/A5029858957","display_name":"Andre\u0131\u030c Kotlov","orcid":null},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Andrei? Kotlov","raw_affiliation_strings":["Department of Mathematics, Yale University, New Haven, CT 06520"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yale University, New Haven, CT 06520","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029858957"],"corresponding_institution_ids":["https://openalex.org/I32971472"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":1.0048,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.7335683,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"26","issue":"1","first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9995999932289124,"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":0.9995999932289124,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9994000196456909,"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":0.9973000288009644,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8620378971099854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8088264465332031},{"id":"https://openalex.org/keywords/windmill-graph","display_name":"Windmill graph","score":0.5376786589622498},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5206705331802368},{"id":"https://openalex.org/keywords/friendship-graph","display_name":"Friendship graph","score":0.5154522061347961},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5057029724121094},{"id":"https://openalex.org/keywords/critical-graph","display_name":"Critical graph","score":0.5001316070556641},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.488920122385025},{"id":"https://openalex.org/keywords/wheel-graph","display_name":"Wheel graph","score":0.47577133774757385},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4613203704357147},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.39090242981910706},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.3496828079223633}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8620378971099854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8088264465332031},{"id":"https://openalex.org/C73380178","wikidata":"https://www.wikidata.org/wiki/Q8024306","display_name":"Windmill graph","level":5,"score":0.5376786589622498},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5206705331802368},{"id":"https://openalex.org/C70488441","wikidata":"https://www.wikidata.org/wiki/Q5504427","display_name":"Friendship graph","level":5,"score":0.5154522061347961},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5057029724121094},{"id":"https://openalex.org/C167750561","wikidata":"https://www.wikidata.org/wiki/Q1789512","display_name":"Critical graph","level":5,"score":0.5001316070556641},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.488920122385025},{"id":"https://openalex.org/C148364342","wikidata":"https://www.wikidata.org/wiki/Q948887","display_name":"Wheel graph","level":5,"score":0.47577133774757385},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4613203704357147},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.39090242981910706},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.3496828079223633}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1097-0118(199709)26:1<1::aid-jgt1>3.0.co;2-n","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199709)26:1<1::aid-jgt1>3.0.co;2-n","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","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":0,"referenced_works":[],"related_works":["https://openalex.org/W3123049420","https://openalex.org/W2080358117","https://openalex.org/W4205905853","https://openalex.org/W2962679774","https://openalex.org/W1989256506","https://openalex.org/W2986347301","https://openalex.org/W2893859033","https://openalex.org/W2321820803","https://openalex.org/W2062344138","https://openalex.org/W2738300330"],"abstract_inverted_index":{"It":[0],"was":[1,40],"proved":[2],"(A.":[3],"Kotlov":[4],"and":[5,10],"L.":[6],"Lov\u00e1sz,":[7],"The":[8],"rank":[9,33],"size":[11],"of":[12,22,34,51],"graphs,":[13],"J.":[14],"Graph":[15,69],"Theory":[16,70],"23(1996),":[17],"185\u2013189)":[18],"that":[19,47],"the":[20,32,35,48],"number":[21,50],"vertices":[23],"in":[24],"a":[25,52],"twin-free":[26],"graph":[27,53],"is":[28,31,54],"where":[29,55],"r":[30],"adjacency":[36],"matrix.":[37],"This":[38],"bound":[39],"shown":[41],"to":[42],"be":[43],"tight.":[44],"We":[45],"show":[46],"chromatic":[49],"$\\Delta":[56],"=":[57],"4/3":[58],"<":[59],"\\sqrt{2}$.":[60],"\u00a9":[61],"1997":[62,73],"John":[63],"Wiley":[64],"&":[65],"Sons,":[66],"Inc.":[67],"J":[68],"26:":[71],"1\u20138,":[72]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}