{"id":"https://openalex.org/W2006160791","doi":"https://doi.org/10.1137/100803869","title":"Packing Triangles in Weighted Graphs","display_name":"Packing Triangles in Weighted Graphs","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2006160791","doi":"https://doi.org/10.1137/100803869","mag":"2006160791"},"language":"en","primary_location":{"id":"doi:10.1137/100803869","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100803869","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027585618","display_name":"Guillaume Chapuy","orcid":"https://orcid.org/0000-0001-7730-5417"},"institutions":[{"id":"https://openalex.org/I4210094115","display_name":"Laboratoire d'Informatique Algorithmique: Fondements et Applications","ror":"https://ror.org/00pbqgm18","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210094115","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Guillaume Chapuy","raw_affiliation_strings":["Laboratoire d'informatique Algorithmique : Fondements et Applications"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d'informatique Algorithmique : Fondements et Applications","institution_ids":["https://openalex.org/I4210094115"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007183588","display_name":"Matt DeVos","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Matt DeVos","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029773109","display_name":"Jessica McDonald","orcid":"https://orcid.org/0000-0001-7648-7968"},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jessica McDonald","raw_affiliation_strings":["[Univ. of Houston]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[Univ. of Houston]","institution_ids":["https://openalex.org/I44461941"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005993212","display_name":"Bojan Mohar","orcid":"https://orcid.org/0000-0002-7408-6148"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Bojan Mohar","raw_affiliation_strings":["Department of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics","institution_ids":["https://openalex.org/I530967"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044834204","display_name":"Diego Scheide","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Diego Scheide","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5027585618"],"corresponding_institution_ids":["https://openalex.org/I4210094115"],"apc_list":null,"apc_paid":null,"fwci":1.4903,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.84365723,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"28","issue":"1","first_page":"226","last_page":"239"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9987000226974487,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8820632696151733},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7853859066963196},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6745489835739136},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6629705429077148},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.530978262424469},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5074676871299744},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.49003851413726807},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.438416063785553},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09775024652481079},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.04868403077125549}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8820632696151733},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7853859066963196},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6745489835739136},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6629705429077148},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.530978262424469},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5074676871299744},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.49003851413726807},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.438416063785553},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09775024652481079},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.04868403077125549},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100803869","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100803869","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:HAL:hal-01185317v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01185317","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Discrete Mathematics, 2014, 28 (1), pp.226--239. ⟨10.1137/100803869⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1969037852","https://openalex.org/W1990901538","https://openalex.org/W1990953773","https://openalex.org/W2002955992","https://openalex.org/W2100437838","https://openalex.org/W2150815458","https://openalex.org/W2327315803"],"related_works":["https://openalex.org/W4256429076","https://openalex.org/W1971174658","https://openalex.org/W2099195351","https://openalex.org/W2348092930","https://openalex.org/W2012063272","https://openalex.org/W3129272755","https://openalex.org/W2138685729","https://openalex.org/W26693340","https://openalex.org/W1963777171","https://openalex.org/W2132864204"],"abstract_inverted_index":{"Tuza":[0],"conjectured":[1],"that":[2,79,99,105],"for":[3],"every":[4],"graph":[5],"$G$":[6],"the":[7,54,86],"maximum":[8],"size":[9,19],"$\\nu$":[10],"of":[11,14,21,24,38,75,89],"a":[12,22,73],"set":[13,23],"edge-disjoint":[15],"triangles":[16,28,47],"and":[17,45,65,91,103],"minimum":[18],"$\\tau$":[20],"edges":[25],"meeting":[26],"all":[27],"satisfy":[29],"$\\tau":[30,80,100],"\\leq":[31,81,101],"2\\nu$.":[32],"We":[33,97],"consider":[34],"an":[35],"edge-weighted":[36],"version":[37,88],"this":[39,63,94,106],"conjecture,":[40],"which":[41],"amounts":[42],"to":[43,59],"packing":[44],"covering":[46],"in":[48,62],"multigraphs.":[49],"Several":[50],"known":[51],"results":[52],"about":[53],"original":[55],"problem":[56],"are":[57,67],"shown":[58],"be":[60],"true":[61],"context,":[64],"some":[66],"improved.":[68],"In":[69],"particular,":[70],"we":[71],"answer":[72],"question":[74],"Krivelevich,":[76],"who":[77],"proved":[78],"2\\nu^*$":[82],"(where":[83],"$\\nu^*$":[84],"is":[85,95,108],"fractional":[87],"$\\nu$)":[90],"asked":[92],"whether":[93],"tight.":[96],"prove":[98],"2\\nu^*-\\frac{1}{\\sqrt{6}}\\sqrt{\\nu^*}$":[102],"show":[104],"bound":[107],"essentially":[109],"best":[110],"possible.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}