{"id":"https://openalex.org/W2020236981","doi":"https://doi.org/10.1002/(sici)1098-2418(199805)12:3<297::aid-rsa5>3.0.co;2-q","title":"An algorithmic version of the blow-up lemma","display_name":"An algorithmic version of the blow-up lemma","publication_year":1998,"publication_date":"1998-05-01","ids":{"openalex":"https://openalex.org/W2020236981","doi":"https://doi.org/10.1002/(sici)1098-2418(199805)12:3<297::aid-rsa5>3.0.co;2-q","mag":"2020236981"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1098-2418(199805)12:3<297::aid-rsa5>3.0.co;2-q","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1098-2418(199805)12:3<297::aid-rsa5>3.0.co;2-q","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"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":"Random Structures and Algorithms","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":null,"display_name":"J\ufffdnos Koml\ufffds","orcid":null},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J\ufffdnos Koml\ufffds","raw_affiliation_strings":["Mathematics Department , Rutgers University , New Brunswick, NJ, 08903"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department , Rutgers University , New Brunswick, NJ, 08903","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087999366","display_name":"G\u00e1bor N. S\u00e1rk\u00f6zy","orcid":null},"institutions":[{"id":"https://openalex.org/I107077323","display_name":"Worcester Polytechnic Institute","ror":"https://ror.org/05ejpqr48","country_code":"US","type":"education","lineage":["https://openalex.org/I107077323"]},{"id":"https://openalex.org/I4210098394","display_name":"Zhejiang Party School","ror":"https://ror.org/00rvyvv90","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210098394"]}],"countries":["CN","US"],"is_corresponding":true,"raw_author_name":"Gabor N. Sarkozy","raw_affiliation_strings":["Computer Science Department, Worcester Polytechnic Institute, Worcester, MA 01609","Part of this paper was written while Sarkozy was visiting MSRI Berkeley, as part of the Combinatorics Program. Research at MSRI is supported in part by NSF grant DMS-9022140"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, Worcester Polytechnic Institute, Worcester, MA 01609","institution_ids":["https://openalex.org/I107077323"]},{"raw_affiliation_string":"Part of this paper was written while Sarkozy was visiting MSRI Berkeley, as part of the Combinatorics Program. Research at MSRI is supported in part by NSF grant DMS-9022140","institution_ids":["https://openalex.org/I4210098394"]}]},{"author_position":"last","author":{"id":null,"display_name":"Endre Szemer\ufffddi","orcid":null},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Endre Szemer\ufffddi","raw_affiliation_strings":["Computer Science Department, Rutgers University, New Brunswick, NJ 08903"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, Rutgers University, New Brunswick, NJ 08903","institution_ids":["https://openalex.org/I102322142"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087999366"],"corresponding_institution_ids":["https://openalex.org/I107077323","https://openalex.org/I4210098394"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":5.8499,"has_fulltext":false,"cited_by_count":86,"citation_normalized_percentile":{"value":0.96617211,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"12","issue":"3","first_page":"297","last_page":"312"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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/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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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/lemma","display_name":"Lemma (botany)","score":0.9249515533447266},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6674498319625854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6283644437789917},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.560943067073822},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5479481220245361},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.49916887283325195},{"id":"https://openalex.org/keywords/probabilistic-method","display_name":"Probabilistic method","score":0.4636377692222595},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4486902356147766},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4415883421897888},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.4299226999282837},{"id":"https://openalex.org/keywords/induced-subgraph-isomorphism-problem","display_name":"Induced subgraph isomorphism problem","score":0.4246065318584442},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.4165025055408478},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.22681191563606262},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.1471472978591919}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.9249515533447266},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6674498319625854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6283644437789917},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.560943067073822},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5479481220245361},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.49916887283325195},{"id":"https://openalex.org/C60782215","wikidata":"https://www.wikidata.org/wiki/Q3333679","display_name":"Probabilistic method","level":3,"score":0.4636377692222595},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4486902356147766},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4415883421897888},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.4299226999282837},{"id":"https://openalex.org/C191241153","wikidata":"https://www.wikidata.org/wiki/Q6027240","display_name":"Induced subgraph isomorphism problem","level":5,"score":0.4246065318584442},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.4165025055408478},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.22681191563606262},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.1471472978591919},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/(sici)1098-2418(199805)12:3<297::aid-rsa5>3.0.co;2-q","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1098-2418(199805)12:3<297::aid-rsa5>3.0.co;2-q","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"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":"Random Structures and Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.137.3694","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.137.3694","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.wpi.edu/~gsarkozy/onlpapers/blowalg.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.96.5010","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.96.5010","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.wpi.edu/~gsarkozy/Cikkek/8.pdf","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/W1551595104","https://openalex.org/W1960909089","https://openalex.org/W1979641885","https://openalex.org/W1984080039","https://openalex.org/W1987001420","https://openalex.org/W1991253503","https://openalex.org/W1993525660","https://openalex.org/W1997802297","https://openalex.org/W2005223884","https://openalex.org/W2017205387","https://openalex.org/W2026143151","https://openalex.org/W2056567608","https://openalex.org/W2062435485","https://openalex.org/W2064398292","https://openalex.org/W2083580384","https://openalex.org/W2100061495","https://openalex.org/W2110963759","https://openalex.org/W2115630228","https://openalex.org/W2116537669","https://openalex.org/W2128452148","https://openalex.org/W2147310610","https://openalex.org/W2157529519","https://openalex.org/W2160743102","https://openalex.org/W2914876264"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1482551403","https://openalex.org/W1097487277","https://openalex.org/W2768610039","https://openalex.org/W2532922352","https://openalex.org/W4308265086","https://openalex.org/W2949943566","https://openalex.org/W2351207523","https://openalex.org/W2020236981","https://openalex.org/W64270857"],"abstract_inverted_index":{"Recently":[0],"we":[1,79],"developed":[2],"a":[3],"new":[4],"method":[5,15],"in":[6,23,60,98,131],"graph":[7],"theory":[8],"based":[9],"on":[10],"the":[11,32,35,39,67,85,104,119,124],"regularity":[12,36],"lemma.":[13,87],"The":[14,26,88],"is":[16,38,69,103],"applied":[17],"to":[18,54,107],"find":[19,55],"certain":[20],"spanning":[21,58],"subgraphs":[22,59],"dense":[24],"graphs.":[25,62],"other":[27],"main":[28],"general":[29],"tool":[30],"of":[31,66,84],"method,":[33],"besides":[34],"lemma,":[37],"so-called":[40],"blow-up":[41,86],"lemma":[42,52,68],"(Koml\u00f3s,":[43],"S\u00e1rk\u00f6zy,":[44],"and":[45,129],"Szemer\u00e9di":[46],"[Combinatorica,":[47],"17,":[48],"109\u2013123":[49],"(1997)].":[50],"This":[51],"helps":[53],"bounded":[56],"degree":[57],"\u03b5-regular":[61],"Our":[63],"original":[64],"proof":[65],"not":[70],"algorithmic,":[71],"it":[72],"applies":[73],"probabilistic":[74],"methods.":[75],"In":[76],"this":[77],"paper":[78],"provide":[80],"an":[81,92],"algorithmic":[82],"version":[83],"desired":[89],"subgraph,":[90],"for":[91],"n-vertex":[93],"graph,":[94],"can":[95,126],"be":[96,127],"found":[97],"time":[99,105],"O(nM(n)),":[100],"where":[101],"M(n)=O(n2.376)":[102],"needed":[106],"multiply":[108],"two":[109],"n":[110,112],"by":[111],"matrices":[113],"with":[114],"0,":[115],"1":[116],"entires":[117],"over":[118],"integers.":[120],"We":[121],"show":[122],"that":[123],"algorithm":[125],"parallelized":[128],"implemented":[130],"NC5.":[132],"\u00a9":[133],"1998":[134,145],"John":[135],"Wiley":[136],"&":[137],"Sons,":[138],"Inc.":[139],"Random":[140],"Struct.":[141],"Alg.,":[142],"12,":[143],"297\u2013312,":[144]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}