{"id":"https://openalex.org/W2008209078","doi":"https://doi.org/10.1142/s1793830910000930","title":"TRIANGLE-FREE 2-MATCHINGS REVISITED","display_name":"TRIANGLE-FREE 2-MATCHINGS REVISITED","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W2008209078","doi":"https://doi.org/10.1142/s1793830910000930","mag":"2008209078"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830910000930","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830910000930","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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/A5037511746","display_name":"Maxim A. Babenko","orcid":null},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"MAXIM BABENKO","raw_affiliation_strings":["Department of Mechanics and Mathematics, Moscow State University, Leninskie Gory, 119991 Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Mechanics and Mathematics, Moscow State University, Leninskie Gory, 119991 Moscow, Russia","institution_ids":["https://openalex.org/I19880235"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078323736","display_name":"Alexey Gusakov","orcid":null},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"ALEXEY GUSAKOV","raw_affiliation_strings":["Department of Mechanics and Mathematics, Moscow State University, Leninskie Gory, 119991 Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Mechanics and Mathematics, Moscow State University, Leninskie Gory, 119991 Moscow, Russia","institution_ids":["https://openalex.org/I19880235"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056565460","display_name":"Ilya Razenshteyn","orcid":null},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"ILYA RAZENSHTEYN","raw_affiliation_strings":["Department of Mechanics and Mathematics, Moscow State University, Leninskie Gory, 119991 Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Mechanics and Mathematics, Moscow State University, Leninskie Gory, 119991 Moscow, Russia","institution_ids":["https://openalex.org/I19880235"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5037511746"],"corresponding_institution_ids":["https://openalex.org/I19880235"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.0927847,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"02","issue":"04","first_page":"643","last_page":"654"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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":0.9994000196456909,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9977999925613403,"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/combinatorics","display_name":"Combinatorics","score":0.7941094040870667},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7195541858673096},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.6314884424209595},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5210044384002686},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41783973574638367}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7941094040870667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7195541858673096},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6314884424209595},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5210044384002686},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41783973574638367},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830910000930","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830910000930","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W37994088","https://openalex.org/W145550941","https://openalex.org/W631645519","https://openalex.org/W1971663478","https://openalex.org/W2053711501","https://openalex.org/W2157529519","https://openalex.org/W2335389215","https://openalex.org/W4236872582"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"A":[0],"2-matching":[1,80,133,201],"in":[2,102,134,202],"an":[3,206,212,225],"undirected":[4],"graph":[5,165,181,252],"G":[6],"=":[7,210,220,231],"(VG,":[8],"EG)":[9],"is":[10,47,64,160],"a":[11,71,76,93,130,142,167,187,198,203,243],"function":[12],"x:":[13],"EG":[14],"\u2192":[15],"{0,":[16],"1,":[17],"2}":[18],"such":[19,248],"that":[20,74,98,162,178,240,249],"for":[21,32,196,208,218,229],"each":[22],"node":[23],"v":[24,38],"\u2208":[25,55],"VG":[26],"the":[27,48,115,119,148,154,193],"sum":[28,49],"of":[29,45,81,121,147,156],"values":[30],"x(e)":[31],"all":[33],"edges":[34],"e":[35,51],"incident":[36],"to":[37,128],"does":[39],"not":[40],"exceed":[41],"2.":[42],"The":[43],"size":[44,82],"x":[46,63],"\u2211":[50],"x(e).":[52],"If":[53],"{e":[54],"EG|x(e)":[56],"\u2260":[57],"0}":[58],"contains":[59,186,253],"no":[60],"triangles":[61],"then":[62],"called":[65],"triangle-free.":[66],"Cornu\u00e9jols":[67],"and":[68,90,123,176,224],"Pulleyblank":[69],"devised":[70],"combinatorial":[72],"O(mn)-algorithm":[73],"finds":[75],"maximum":[77,131],"triangle":[78],"free":[79],"(hereinafter":[83],"n":[84,215,257],"\u2254":[85,88],"|VG|,":[86],"m":[87],"|EG|)":[89],"also":[91,238],"established":[92],"min-max":[94,149],"theorem.":[95,150],"We":[96,191,237],"claim":[97],"this":[99,174],"approach":[100],"is,":[101],"fact,":[103],"superfluous":[104],"by":[105],"demonstrating":[106],"how":[107],"these":[108],"results":[109],"may":[110],"be":[111],"obtained":[112],"directly":[113],"from":[114],"Edmonds\u2013Gallai":[116],"decomposition.":[117],"Applying":[118],"algorithm":[120],"Micali":[122],"Vazirani":[124],"we":[125,140,152],"are":[126],"able":[127],"find":[129],"triangle-free":[132,189,200,259],"[Formula:":[135],"see":[136],"text]":[137],"time.":[138],"Also":[139],"give":[141,192],"short":[143],"self-contained":[144],"algorithmic":[145],"proof":[146],"Next,":[151],"consider":[153],"case":[155],"regular":[157,164],"graphs.":[158],"It":[159],"well-known":[161],"every":[163,179,250],"admits":[166],"perfect":[168,188,199,258],"2-matching.":[169,190],"One":[170],"can":[171],"easily":[172],"strengthen":[173],"result":[175],"prove":[177,239],"d-regular":[180,204],"(for":[182],"d":[183,209,219,230],"\u2265":[184,222,235],"3)":[185],"following":[194],"algorithms":[195],"finding":[197],"graph:":[205],"O(n)-algorithm":[207],"3,":[211],"O(m":[213],"+":[214,233],"3/2":[216],")-algorithm":[217,228],"2k(k":[221],"2),":[223],"O(n":[226],"2":[227],"2k":[232],"1(k":[234],"2).":[236],"there":[241],"exists":[242],"constant":[244],"c":[245,256],"&gt;":[246],"1":[247],"3-regular":[251],"at":[254],"least":[255],"2-matchings.":[260]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
