{"id":"https://openalex.org/W1902204033","doi":"https://doi.org/10.37236/523","title":"Sharp Threshold Functions for Random Intersection Graphs via a Coupling Method","display_name":"Sharp Threshold Functions for Random Intersection Graphs via a Coupling Method","publication_year":2011,"publication_date":"2011-02-14","ids":{"openalex":"https://openalex.org/W1902204033","doi":"https://doi.org/10.37236/523","mag":"1902204033"},"language":"en","primary_location":{"id":"doi:10.37236/523","is_oa":true,"landing_page_url":"https://doi.org/10.37236/523","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p36/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":true,"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":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p36/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002490455","display_name":"Katarzyna Rybarczyk","orcid":"https://orcid.org/0000-0002-3998-6482"},"institutions":[{"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"],"is_corresponding":true,"raw_author_name":"Katarzyna Rybarczyk","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 60-769 Pozna, Poland","Adam Mickiewicz University in Pozna\u0144)"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 60-769 Pozna, Poland","institution_ids":["https://openalex.org/I59411706"]},{"raw_affiliation_string":"Adam Mickiewicz University in Pozna\u0144)","institution_ids":["https://openalex.org/I59411706"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002490455"],"corresponding_institution_ids":["https://openalex.org/I59411706"],"apc_list":null,"apc_paid":null,"fwci":4.6004,"has_fulltext":true,"cited_by_count":52,"citation_normalized_percentile":{"value":0.94906542,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"18","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9994000196456909,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994000196456909,"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/mathematics","display_name":"Mathematics","score":0.7753570675849915},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.7653137445449829},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6377495527267456},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5476332306861877},{"id":"https://openalex.org/keywords/containment","display_name":"Containment (computer programming)","score":0.5104367136955261},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5092254877090454},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.4796655476093292},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.47511348128318787},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.45898565649986267},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43104711174964905},{"id":"https://openalex.org/keywords/intersection-number","display_name":"Intersection number","score":0.42871659994125366},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.21797245740890503},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12957489490509033},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10256069898605347},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07495424151420593}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7753570675849915},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.7653137445449829},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6377495527267456},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5476332306861877},{"id":"https://openalex.org/C2777019822","wikidata":"https://www.wikidata.org/wiki/Q390066","display_name":"Containment (computer programming)","level":2,"score":0.5104367136955261},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5092254877090454},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.4796655476093292},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.47511348128318787},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.45898565649986267},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43104711174964905},{"id":"https://openalex.org/C103368685","wikidata":"https://www.wikidata.org/wiki/Q638846","display_name":"Intersection number","level":3,"score":0.42871659994125366},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.21797245740890503},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12957489490509033},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10256069898605347},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07495424151420593},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"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/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/523","is_oa":true,"landing_page_url":"https://doi.org/10.37236/523","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p36/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":true,"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:10.1.1.601.6955","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.601.6955","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_18/PDF/v18i1p36.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/523","is_oa":true,"landing_page_url":"https://doi.org/10.37236/523","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p36/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":true,"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/W1902204033.pdf","grobid_xml":"https://content.openalex.org/works/W1902204033.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W188357332","https://openalex.org/W630423399","https://openalex.org/W1489878404","https://openalex.org/W1497703977","https://openalex.org/W1606180716","https://openalex.org/W1998025836","https://openalex.org/W2023212718","https://openalex.org/W2031211633","https://openalex.org/W2061726431","https://openalex.org/W2074401061","https://openalex.org/W2165064763","https://openalex.org/W2798655805","https://openalex.org/W3125177404","https://openalex.org/W3144881883","https://openalex.org/W4231513332","https://openalex.org/W4251418041","https://openalex.org/W4388258552"],"related_works":["https://openalex.org/W4287117052","https://openalex.org/W2157783000","https://openalex.org/W3176308333","https://openalex.org/W4206705200","https://openalex.org/W2966902162","https://openalex.org/W2028363955","https://openalex.org/W1893557706","https://openalex.org/W4214565117","https://openalex.org/W2407722793","https://openalex.org/W1527735759"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2],"new":[3],"method":[4,20],"which":[5],"enables":[6],"us":[7],"to":[8,23],"find":[9],"threshold":[10,26],"functions":[11,27],"for":[12,32],"many":[13],"properties":[14],"in":[15,28],"random":[16,29],"intersection":[17,30],"graphs.":[18],"This":[19],"is":[21],"used":[22],"establish":[24],"sharp":[25],"graphs":[31],"$k$\u2013connectivity,":[33],"perfect":[34],"matching":[35],"containment":[36],"and":[37],"Hamilton":[38],"cycle":[39],"containment.":[40]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}