{"id":"https://openalex.org/W3042166040","doi":"https://doi.org/10.1137/20m1351771","title":"Closing the Random Graph Gap in Tuza's Conjecture through the Online Triangle Packing Process","display_name":"Closing the Random Graph Gap in Tuza's Conjecture through the Online Triangle Packing Process","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3042166040","doi":"https://doi.org/10.1137/20m1351771","mag":"3042166040"},"language":"en","primary_location":{"id":"doi:10.1137/20m1351771","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1351771","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2007.04478","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025184846","display_name":"Patrick Bennett","orcid":"https://orcid.org/0000-0003-3147-4690"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Patrick Bennett","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068482277","display_name":"Ryan Cushman","orcid":"https://orcid.org/0000-0003-1792-3875"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ryan Cushman","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5048565272","display_name":"Andrzej Dudek","orcid":"https://orcid.org/0000-0002-6410-5413"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrzej Dudek","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025184846"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0897281,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":"3","first_page":"2145","last_page":"2169"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.996399998664856,"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/T11476","display_name":"Graph theory and applications","score":0.9958000183105469,"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/conjecture","display_name":"Conjecture","score":0.8499202132225037},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8276562690734863},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7135031223297119},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5085152387619019},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.4770319163799286},{"id":"https://openalex.org/keywords/closing","display_name":"Closing (real estate)","score":0.453927218914032},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3472212553024292}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8499202132225037},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8276562690734863},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7135031223297119},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5085152387619019},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.4770319163799286},{"id":"https://openalex.org/C2778775528","wikidata":"https://www.wikidata.org/wiki/Q5135432","display_name":"Closing (real estate)","level":2,"score":0.453927218914032},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3472212553024292},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1351771","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1351771","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2007.04478","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.04478","pdf_url":"https://arxiv.org/pdf/2007.04478","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3042166040","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2007.04478","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2007.04478","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2007.04478","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2007.04478","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.04478","pdf_url":"https://arxiv.org/pdf/2007.04478","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2359628979","display_name":null,"funder_award_id":"426894","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G2690323053","display_name":null,"funder_award_id":"522400","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"}],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3042166040.pdf","grobid_xml":"https://content.openalex.org/works/W3042166040.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W5090298","https://openalex.org/W1531317993","https://openalex.org/W1556797074","https://openalex.org/W1890577096","https://openalex.org/W1969037852","https://openalex.org/W1971994465","https://openalex.org/W1990953773","https://openalex.org/W1999678910","https://openalex.org/W2020243626","https://openalex.org/W2033447978","https://openalex.org/W2051071716","https://openalex.org/W2058108962","https://openalex.org/W2083459869","https://openalex.org/W2103012681","https://openalex.org/W2106456894","https://openalex.org/W2134771417","https://openalex.org/W2155295958","https://openalex.org/W2167969281","https://openalex.org/W2279054828","https://openalex.org/W2323526206","https://openalex.org/W2964282678","https://openalex.org/W2994753695","https://openalex.org/W3045198963","https://openalex.org/W3100754310","https://openalex.org/W3144881883","https://openalex.org/W4233413206"],"related_works":["https://openalex.org/W3201113189","https://openalex.org/W2898354440","https://openalex.org/W2997615180","https://openalex.org/W2768594358","https://openalex.org/W1556797074","https://openalex.org/W3123433281","https://openalex.org/W2994753695","https://openalex.org/W1969037852","https://openalex.org/W3040914542","https://openalex.org/W3093231953","https://openalex.org/W2964282678","https://openalex.org/W2972338096","https://openalex.org/W3143259507","https://openalex.org/W3004209807","https://openalex.org/W2076007465","https://openalex.org/W1612865380","https://openalex.org/W2007095822","https://openalex.org/W2113784155","https://openalex.org/W3049385695","https://openalex.org/W2521224986"],"abstract_inverted_index":{"A":[0],"long-standing":[1],"conjecture":[2,65],"of":[3,32,35,50,53,76],"Zsolt":[4],"Tuza":[5],"asserts":[6],"that":[7,63],"the":[8,17,23,29,41,47,68,79,106,124],"triangle":[9,18,24,42,108,114],"covering":[10,43],"number":[11,20,26,44],"$\u03c4(G)$":[12,45],"is":[13,28,46],"at":[14],"most":[15],"twice":[16],"packing":[19,25,109,115],"$\u03bd(G)$,":[21],"where":[22],"$\u03bd(G)$":[27],"maximum":[30],"size":[31,49],"a":[33,51,101,113],"set":[34,52],"edge-disjoint":[36],"triangles":[37],"in":[38,67,81,116],"$G$":[39],"and":[40,96,118],"minimal":[48],"edges":[54],"intersecting":[55],"all":[56,74],"triangles.":[57],"In":[58],"this":[59,87,120],"paper,":[60],"we":[61],"prove":[62],"Tuza's":[64],"holds":[66],"Erd\u0151s-R\u00e9nyi":[69],"random":[70,102],"graph":[71],"$G(n,m)$":[72,117],"for":[73],"range":[75],"$m$,":[77],"closing":[78],"gap":[80],"what":[82],"was":[83,89],"previously":[84],"known.":[85],"(Recently,":[86],"result":[88],"also":[90],"independently":[91],"proved":[92],"by":[93,122],"Jeff":[94],"Kahn":[95],"Jinyoung":[97],"Park.)":[98],"We":[99],"employ":[100],"greedy":[103],"process":[104,110,121],"called":[105],"online":[107],"to":[111],"produce":[112],"analyze":[119],"using":[123],"differential":[125],"equations":[126],"method.":[127]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
