{"id":"https://openalex.org/W2120693270","doi":"https://doi.org/10.37236/1323","title":"On cycles in the coprime graph of integers","display_name":"On cycles in the coprime graph of integers","publication_year":1996,"publication_date":"1996-12-02","ids":{"openalex":"https://openalex.org/W2120693270","doi":"https://doi.org/10.37236/1323","mag":"2120693270"},"language":"en","primary_location":{"id":"doi:10.37236/1323","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1323","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v4i2r8/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/v4i2r8/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077107126","display_name":"Paul Erd\u0151s","orcid":null},"institutions":[{"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"],"is_corresponding":false,"raw_author_name":"Paul Erd\u0151s","raw_affiliation_strings":["Hungarian Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hungarian Academy of Sciences","institution_ids":["https://openalex.org/I7597260"]}]},{"author_position":"last","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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gabor N. Sarkozy","raw_affiliation_strings":["Worcester Polytechnic Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Worcester Polytechnic Institute","institution_ids":["https://openalex.org/I107077323"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.54,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.82457879,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"4","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9980999827384949,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9980000257492065,"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/coprime-integers","display_name":"Coprime integers","score":0.962741494178772},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9008907675743103},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.848530113697052},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6754149198532104},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6470005512237549},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4325326681137085},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.42846739292144775}],"concepts":[{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.962741494178772},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9008907675743103},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.848530113697052},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6754149198532104},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6470005512237549},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4325326681137085},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.42846739292144775},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1323","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1323","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v4i2r8/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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.18.1214","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.1214","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_4/PDF/v4i2r08.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.39.4256","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.4256","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_4/PostScriptfiles/v4i2r08.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1323","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1323","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v4i2r8/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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2120693270.pdf","grobid_xml":"https://content.openalex.org/works/W2120693270.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W39515261","https://openalex.org/W63284382","https://openalex.org/W91574864","https://openalex.org/W606453859","https://openalex.org/W1981073110","https://openalex.org/W2031583134","https://openalex.org/W2039078154","https://openalex.org/W2057182494","https://openalex.org/W2073511455","https://openalex.org/W2081708172","https://openalex.org/W2100019642","https://openalex.org/W3175367423"],"related_works":["https://openalex.org/W2040038883","https://openalex.org/W2849529886","https://openalex.org/W2374154560","https://openalex.org/W2382727118","https://openalex.org/W2764518425","https://openalex.org/W2369152922","https://openalex.org/W3179849411","https://openalex.org/W2378932980","https://openalex.org/W2377593104","https://openalex.org/W1965894940"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"study":[4],"cycles":[5],"in":[6],"the":[7,16,28,60],"coprime":[8,61],"graph":[9,62],"of":[10,18,75],"integers.":[11],"We":[12,38],"denote":[13],"by":[14,64],"$f(n,k)$":[15],"number":[17],"positive":[19,83],"integers":[20],"$m\\leq":[21],"n$":[22],"with":[23,55],"a":[24,43,69,73],"prime":[25],"factor":[26],"among":[27],"first":[29],"$k$":[30],"primes.":[31],"(If":[32],"$6|n,$":[33],"then":[34,59],"$f(n,2)={{2n}\\over":[35],"{3}}":[36],"$.)":[37],"show":[39],"that":[40,47],"there":[41],"exists":[42],"constant":[44],"$c$":[45],"such":[46],"if":[48],"$A\\subset":[49],"\\{1,":[50],"2,":[51],"\\ldots":[52],",":[53],"n\\}$":[54],"$|A|":[56],">":[57],"f(n,2),$":[58],"induced":[63],"$A$":[65],"not":[66],"only":[67],"contains":[68],"triangle,":[70],"but":[71],"also":[72],"cycle":[74],"length":[76],"$2":[77],"l":[78],"+":[79],"1$":[80],"for":[81],"every":[82],"integer":[84],"$l\\leq":[85],"c":[86],"n":[87],".$":[88]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}