{"id":"https://openalex.org/W1562960078","doi":"https://doi.org/10.37236/1618","title":"Holes in Graphs","display_name":"Holes in Graphs","publication_year":2001,"publication_date":"2001-10-14","ids":{"openalex":"https://openalex.org/W1562960078","doi":"https://doi.org/10.37236/1618","mag":"1562960078"},"language":"en","primary_location":{"id":"doi:10.37236/1618","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1618","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r1/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r1/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010855963","display_name":"Yuejian Peng","orcid":"https://orcid.org/0000-0002-0243-0691"},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]},{"id":"https://openalex.org/I59411706","display_name":"Adam Mickiewicz University in Pozna\u0144","ror":"https://ror.org/04g6bbq64","country_code":"PL","type":"education","lineage":["https://openalex.org/I59411706"]}],"countries":["PL","US"],"is_corresponding":false,"raw_author_name":"Yuejian Peng","raw_affiliation_strings":["Department of Mathematics and Computer Science Emory University, Atlanta, USA","Department of Discrete Mathematics Adam Mickiewicz University, Pozna\u0144, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science Emory University, Atlanta, USA","institution_ids":["https://openalex.org/I150468666"]},{"raw_affiliation_string":"Department of Discrete Mathematics Adam Mickiewicz University, Pozna\u0144, Poland","institution_ids":["https://openalex.org/I59411706"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109078443","display_name":"Vojt\u011bch R\u00f6dl","orcid":null},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]},{"id":"https://openalex.org/I59411706","display_name":"Adam Mickiewicz University in Pozna\u0144","ror":"https://ror.org/04g6bbq64","country_code":"PL","type":"education","lineage":["https://openalex.org/I59411706"]}],"countries":["PL","US"],"is_corresponding":false,"raw_author_name":"Vojtech R\u00f6dl","raw_affiliation_strings":["Department of Mathematics and Computer Science Emory University, Atlanta, USA","Department of Discrete Mathematics Adam Mickiewicz University, Pozna\u0144, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science Emory University, Atlanta, USA","institution_ids":["https://openalex.org/I150468666"]},{"raw_affiliation_string":"Department of Discrete Mathematics Adam Mickiewicz University, Pozna\u0144, Poland","institution_ids":["https://openalex.org/I59411706"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078267731","display_name":"Andrzej Ruci\u0144ski","orcid":"https://orcid.org/0000-0002-0742-7694"},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]},{"id":"https://openalex.org/I59411706","display_name":"Adam Mickiewicz University in Pozna\u0144","ror":"https://ror.org/04g6bbq64","country_code":"PL","type":"education","lineage":["https://openalex.org/I59411706"]}],"countries":["PL","US"],"is_corresponding":false,"raw_author_name":"Andrzej Ruci\u0144ski","raw_affiliation_strings":["Department of Mathematics and Computer Science Emory University, Atlanta, USA","Department of Discrete Mathematics Adam Mickiewicz University, Pozna\u0144, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science Emory University, Atlanta, USA","institution_ids":["https://openalex.org/I150468666"]},{"raw_affiliation_string":"Department of Discrete Mathematics Adam Mickiewicz University, Pozna\u0144, Poland","institution_ids":["https://openalex.org/I59411706"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6144,"has_fulltext":true,"cited_by_count":40,"citation_normalized_percentile":{"value":0.56563707,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"9","issue":"1","first_page":null,"last_page":null},"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":0.9966999888420105,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9965999722480774,"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":0.8036216497421265},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7944391965866089},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6021351218223572},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5193684697151184},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.49950575828552246},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4362945854663849},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41998034715652466}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8036216497421265},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7944391965866089},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6021351218223572},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5193684697151184},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.49950575828552246},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4362945854663849},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41998034715652466},{"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/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":1,"locations":[{"id":"doi:10.37236/1618","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1618","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r1/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/1618","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1618","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r1/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2364055859","display_name":"Research in Combinatorics","funder_award_id":"9704114","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309381","display_name":"Emory University","ror":"https://ror.org/03czfpz43"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1562960078.pdf","grobid_xml":"https://content.openalex.org/works/W1562960078.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1538750443","https://openalex.org/W1551595104","https://openalex.org/W1906724808","https://openalex.org/W1981338295","https://openalex.org/W2057452136","https://openalex.org/W2159101505","https://openalex.org/W3144881883"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1097487277","https://openalex.org/W2768610039","https://openalex.org/W4308265086","https://openalex.org/W2949964783","https://openalex.org/W2106889256","https://openalex.org/W2801357573","https://openalex.org/W2735923117","https://openalex.org/W2115913661","https://openalex.org/W3168772390"],"abstract_inverted_index":{"The":[0],"celebrated":[1],"Regularity":[2],"Lemma":[3],"of":[4,23,94],"Szemer\u00e9di":[5],"asserts":[6],"that":[7,20,74],"every":[8,75],"sufficiently":[9],"large":[10],"graph":[11,34,66,76],"$G$":[12,35],"can":[13,59],"be":[14,38,60],"partitioned":[15],"in":[16],"such":[17],"a":[18,55,81,91,105],"way":[19],"most":[21],"pairs":[22],"the":[24,33,41,64],"partition":[25,42],"sets":[26,43],"span":[27],"$\\epsilon$-regular":[28,51,85],"subgraphs.":[29],"In":[30,69],"applications,":[31],"however,":[32],"has":[36],"to":[37,104],"dense":[39,84],"and":[40],"are":[44],"typically":[45],"very":[46],"small.":[47],"If":[48],"only":[49],"one":[50,58],"pair":[52],"is":[53,67],"needed,":[54],"much":[56],"bigger":[57],"found,":[61],"even":[62],"if":[63],"original":[65],"sparse.":[68],"this":[70],"paper":[71],"we":[72],"show":[73],"with":[77],"density":[78],"$d$":[79],"contains":[80],"large,":[82],"relatively":[83],"pair.":[86],"We":[87],"mainly":[88],"focus":[89],"on":[90],"related":[92],"concept":[93],"an":[95],"$(\\epsilon,\\sigma)$-dense":[96],"pair,":[97],"for":[98],"which":[99],"our":[100],"bound":[101],"is,":[102],"up":[103],"constant,":[106],"best":[107],"possible.":[108]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-25T09:21:30.201066","created_date":"2016-06-24T00:00:00"}