{"id":"https://openalex.org/W2100948098","doi":"https://doi.org/10.1017/s0963548308009206","title":"G-Intersection Theorems for Matchings and Other Graphs","display_name":"G-Intersection Theorems for Matchings and Other Graphs","publication_year":2008,"publication_date":"2008-07-01","ids":{"openalex":"https://openalex.org/W2100948098","doi":"https://doi.org/10.1017/s0963548308009206","mag":"2100948098"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548308009206","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics, Probability & Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://www.ucl.ac.uk/~ucahjmt/gint.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010629356","display_name":"J. Robert Johnson","orcid":null},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"J. robert Johnson","raw_affiliation_string":"School of mathematical sciences, queen mary, university of london, london e1 4ns, uk (e-mail: r.johnson@qmul.ac.uk)","raw_affiliation_strings":["School of mathematical sciences, queen mary, university of london, london e1 4ns, uk (e-mail: r.johnson@qmul.ac.uk)"]},{"author_position":"last","author":{"id":"https://openalex.org/A5002343159","display_name":"John Talbot","orcid":null},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"John Talbot","raw_affiliation_string":"Department of mathematics, university college london, london wc1e 6bt, uk (e-mail: talbot@math.ucl.ac.uk)","raw_affiliation_strings":["Department of mathematics, university college london, london wc1e 6bt, uk (e-mail: talbot@math.ucl.ac.uk)"]}],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":4,"cited_by_percentile_year":{"min":80,"max":82},"biblio":{"volume":"17","issue":"4","first_page":"559","last_page":"575"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9999,"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":0.9999,"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":"Graph Theory and Algorithms","score":0.9996,"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/T12056","display_name":"Bayesian Monte Carlo Methods in Scientific Inference","score":0.9915,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"keyword":"matchings","score":0.5281},{"keyword":"graphs","score":0.4585}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8784092},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7524292},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6366223},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5147252},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49710372},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4625169},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05682239},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548308009206","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics, Probability & Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.1708","pdf_url":"http://www.ucl.ac.uk/~ucahjmt/gint.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.1708","pdf_url":"http://www.ucl.ac.uk/~ucahjmt/gint.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"referenced_works_count":5,"referenced_works":["https://openalex.org/W1999678910","https://openalex.org/W2019935404","https://openalex.org/W2028845083","https://openalex.org/W3105783410","https://openalex.org/W4233413206"],"related_works":["https://openalex.org/W2348909947","https://openalex.org/W4292672442","https://openalex.org/W2362101859","https://openalex.org/W2941610985","https://openalex.org/W2791431590","https://openalex.org/W1978900583","https://openalex.org/W2350688482","https://openalex.org/W2053575972","https://openalex.org/W4323256314","https://openalex.org/W2087777635"],"ngrams_url":"https://api.openalex.org/works/W2100948098/ngrams","abstract_inverted_index":{"If":[0],"G":[1,42,53,113,139,221,230],"is":[2,14,89,103,114,156,176],"a":[3,31,40,50,90,104,115,133],"graph":[4],"with":[5],"vertex":[6],"set":[7],"[":[8],"n":[9,84,155,158,164,168,197],"]":[10],"then":[11,193],"$\\mathcal{A}\\subseteq":[12],"2^{[n]}$":[13],"G-intersecting":[15],"if,":[16],"for":[17,73,136],"all":[18,145],"$A,B\\in":[19],"\\mathcal{A}$":[20],",":[21],"either":[22],"A":[23,33],"\u2229":[24],"B":[25,37],"\u2260":[26],"\u2205":[27],"or":[28],"there":[29,88,102],"exist":[30],"\u2208":[32,36],"and":[34,65,83,85,107,160,210],"b":[35,43],"such":[38],"that":[39,101,123,152,212],"~":[41],".":[44,174,175,203,231],"The":[45],"question":[46],"of":[47,81,181,218,229],"how":[48],"large":[49],"k":[51,82,146,161],"-uniform":[52],"-intersecting":[54,140,198,222],"family":[55,141,199,223],"can":[56,127],"be":[57],"was":[58],"first":[59,98],"considered":[60],"by":[61],"Bohman,":[62],"Frieze,":[63],"Ruszink\u00f3":[64],"Thoma":[66],"[2],":[67],"who":[68],"identified":[69],"two":[70],"natural":[71],"candidates":[72],"the":[74,78,95,109,137,157,177,194,207,216,219,226],"extrema":[75],"depending":[76],"on":[77,225],"relative":[79],"sizes":[80],"asked":[86],"whether":[87],"sharp":[91,105],"phase":[92],"transition":[93,106],"between":[94],"two.":[96],"Our":[97,129],"result":[99,131],"shows":[100],"characterizes":[108],"extremal":[110,125],"families":[111,126],"when":[112],"matching.":[116],"We":[117],"also":[118],"give":[119],"an":[120],"example":[121],"demonstrating":[122],"other":[124],"occur.":[128],"second":[130],"gives":[132],"sufficient":[134],"condition":[135],"largest":[138,195,220],"to":[142],"contain":[143],"almost":[144],"-sets.":[147],"In":[148],"particular":[149],"we":[150,205],"show":[151,211],"if":[153],"C":[154,196],"-cycle":[159],">":[162],"\u03b1":[163,171],"+":[165,188],"o":[166],"(":[167],"),":[169],"where":[170],"=":[172,191],"0.266.":[173],"smallest":[178],"positive":[179],"root":[180],"(1":[182,187],"\u2212":[183],"x":[184,189],")":[185,190],"3":[186],"1/2,":[192],"has":[200],"size":[201,217],"$(1-o(1))\\binom{n}{k}$":[202],"Finally":[204],"consider":[206],"non-uniform":[208],"problem,":[209],"in":[213],"this":[214],"case":[215],"depends":[224],"matching":[227],"number":[228]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2100948098","counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2024-03-21T13:49:22.088600","created_date":"2016-06-24"}