{"id":"https://openalex.org/W4240119042","doi":"https://doi.org/10.1137/1.9781611974331.ch122","title":"An Algorithmic Hypergraph Regularity Lemma","display_name":"An Algorithmic Hypergraph Regularity Lemma","publication_year":2015,"publication_date":"2015-12-21","ids":{"openalex":"https://openalex.org/W4240119042","doi":"https://doi.org/10.1137/1.9781611974331.ch122"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1137/1.9781611974331.ch122","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/1.9781611974331.ch122","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"proceedings-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/1.9781611974331.ch122","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089503234","display_name":"Brendan Nagle","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brendan Nagle","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109078443","display_name":"Vojt\u011bch R\u00f6dl","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vojt\u011bch R\u00f6dl","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5048188412","display_name":"Mathias Schacht","orcid":"https://orcid.org/0000-0003-1762-4090"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mathias Schacht","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":66},"biblio":{"volume":null,"issue":null,"first_page":"1765","last_page":"1773"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9992,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9992,"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":0.9979,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.997,"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":0.8663015},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.84506},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.7045464},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.50831455}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.8663015},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.84506},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.7045464},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.693043},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6774813},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.66559565},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.62726873},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5643271},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.56099683},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5592167},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.50831455},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43113694},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14544988},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1137/1.9781611974331.ch122","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/1.9781611974331.ch122","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1137/1.9781611974331.ch122","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/1.9781611974331.ch122","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4304755296","https://openalex.org/W4295571831","https://openalex.org/W4221036368","https://openalex.org/W3121250382","https://openalex.org/W2950157558","https://openalex.org/W2526197252","https://openalex.org/W2176262501","https://openalex.org/W2163453622","https://openalex.org/W2085708731","https://openalex.org/W1998171255"],"abstract_inverted_index":{"Szemer\u00e9di's":[0],"Regularity":[1,70,129],"Lemma":[2,71,130],"[22,":[3],"23]":[4],"is":[5],"a":[6,20,63],"powerful":[7],"tool":[8],"in":[9],"graph":[10,112],"theory.":[11],"It":[12],"asserts":[13],"that":[14],"all":[15,114],"large":[16,68],"graphs":[17],"G":[18],"admit":[19],"bounded":[21],"partition":[22,65],"of":[23,27,39,115,126],"E(G),":[24],"most":[25],"classes":[26],"which":[28,57],"are":[29,118],"bipartite":[30],"subgraphs":[31],"with":[32],"uniformly":[33],"distributed":[34],"edges.":[35],"The":[36],"original":[37],"proof":[38,46],"this":[40,96],"result":[41,97],"was":[42,47,72],"non-constructive.":[43,119],"A":[44],"constructive":[45],"given":[48],"by":[49,76],"Alon,":[50],"Duke,":[51],"Lefmann,":[52],"R\u00f6dl":[53,81,91],"and":[54,80,90,92],"Yuster":[55],"[1],":[56],"allows":[58],"one":[59,84],"to":[60,74,87,98,110],"efficiently":[61],"construct":[62],"regular":[64],"for":[66,131],"any":[67],"graph.Szemer\u00e9di's":[69],"extended":[73,95],"hypergraphs":[75],"various":[77],"authors.":[78],"Frankl":[79],"[3]":[82],"gave":[83,105],"such":[85,107],"extension":[86],"3-uniform":[88],"hypergraphs,":[89],"Skokan":[93],"[19]":[94],"k-uniform":[99,132],"hypergraphs.":[100,133],"W.T.":[101],"Gowers":[102],"[4,":[103],"5]":[104],"another":[106],"extension.":[108],"Similarly":[109],"the":[111,127],"case,":[113],"these":[116],"proofs":[117],"We":[120],"present":[121],"an":[122],"efficient":[123],"algorithmic":[124],"version":[125],"Hypergraph":[128]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4240119042","counts_by_year":[],"updated_date":"2024-12-12T11:39:45.939325","created_date":"2022-05-12"}