{"id":"https://openalex.org/W2006135590","doi":"https://doi.org/10.1017/s0963548300001814","title":"An Upper Bound on Zarankiewicz' Problem","display_name":"An Upper Bound on Zarankiewicz' Problem","publication_year":1996,"publication_date":"1996-03-01","ids":{"openalex":"https://openalex.org/W2006135590","doi":"https://doi.org/10.1017/s0963548300001814","mag":"2006135590"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548300001814","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548300001814","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","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/A5023439517","display_name":"Zolt\u00e1n F\u00fcredi","orcid":"https://orcid.org/0000-0001-7335-991X"},"institutions":[{"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/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"government","lineage":["https://openalex.org/I7597260"]}],"countries":["HU","US"],"is_corresponding":true,"raw_author_name":"Zolt\u00e1n F\u00fcredi","raw_affiliation_strings":["Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801-2975, USA and Mathematical Institute of the Hungarian Academy of Sciences, PO Box 127, Budapest 1364, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801-2975, USA and Mathematical Institute of the Hungarian Academy of Sciences, PO Box 127, Budapest 1364, Hungary","institution_ids":["https://openalex.org/I157725225","https://openalex.org/I7597260"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023439517"],"corresponding_institution_ids":["https://openalex.org/I157725225","https://openalex.org/I7597260"],"apc_list":null,"apc_paid":null,"fwci":2.1021,"has_fulltext":false,"cited_by_count":118,"citation_normalized_percentile":{"value":0.83242824,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"5","issue":"1","first_page":"29","last_page":"33"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11476","display_name":"Graph theory and applications","score":0.9976999759674072,"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":0.9948999881744385,"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":0.7740307450294495},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6494012475013733},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6229323148727417},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6008303165435791},{"id":"https://openalex.org/keywords/asymptotically-optimal-algorithm","display_name":"Asymptotically optimal algorithm","score":0.43743598461151123},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4110725522041321},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.13150256872177124},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05917343497276306}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7740307450294495},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6494012475013733},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6229323148727417},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6008303165435791},{"id":"https://openalex.org/C181789720","wikidata":"https://www.wikidata.org/wiki/Q4812191","display_name":"Asymptotically optimal algorithm","level":2,"score":0.43743598461151123},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4110725522041321},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.13150256872177124},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05917343497276306}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548300001814","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548300001814","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320311089","display_name":"National Security Agency","ror":"https://ror.org/0047bvr32"},{"id":"https://openalex.org/F4320326184","display_name":"Hungarian Science Foundation","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W111038805","https://openalex.org/W788200807","https://openalex.org/W795302121","https://openalex.org/W812359745","https://openalex.org/W1444168583","https://openalex.org/W1510730180","https://openalex.org/W1991488719","https://openalex.org/W2009852526","https://openalex.org/W2016480989","https://openalex.org/W2024503125","https://openalex.org/W2080305978","https://openalex.org/W2111007781","https://openalex.org/W2134754301","https://openalex.org/W3142570770"],"related_works":["https://openalex.org/W2163788280","https://openalex.org/W3148718598","https://openalex.org/W2980963558","https://openalex.org/W2012749513","https://openalex.org/W2002282073","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2008268605","https://openalex.org/W1557064786","https://openalex.org/W1647069448"],"abstract_inverted_index":{"Let":[0],"ex(":[1],"n,":[2],"K":[3,14,41],"3,3":[4,15,42],")":[5],"denote":[6],"the":[7],"maximum":[8],"number":[9],"of":[10,12,24],"edges":[11],"a":[13,39],"-free":[16,43],"graph":[17,44],"on":[18,30],"n":[19],"vertices.":[20],"Improving":[21],"earlier":[22],"results":[23],"K\u0151v\u00e1ri,":[25],"T.":[26],"S\u00f3s":[27],"and":[28],"Tur\u00e1n":[29],"Zarankiewicz'":[31],"problem,":[32],"we":[33],"obtain":[34],"that":[35],"Brown's":[36],"example":[37],"for":[38],"maximal":[40],"is":[45],"asymptotically":[46],"optimal.":[47],"Hence":[48],".":[49]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":5}],"updated_date":"2026-05-28T09:10:13.091523","created_date":"2025-10-10T00:00:00"}