{"id":"https://openalex.org/W2060706530","doi":"https://doi.org/10.1137/s0895480100370797","title":"On the Co-<i>P</i><sub>3</sub> -Structure of Perfect Graphs","display_name":"On the Co-<i>P</i><sub>3</sub> -Structure of Perfect Graphs","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2060706530","doi":"https://doi.org/10.1137/s0895480100370797","mag":"2060706530"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480100370797","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480100370797","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/A5088012278","display_name":"Ch\u0131\u0301nh T. Ho\u00e0ng","orcid":"https://orcid.org/0000-0001-6782-1194"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ch\u00ednh T. Ho\u00e0ng","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108103165","display_name":"Bruce Reed","orcid":"https://orcid.org/0009-0002-5656-8941"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Bruce Reed","raw_affiliation_strings":["School of Computer Science, McGill University, Montreal, Quebec, Canada. 571"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, McGill University, Montreal, Quebec, Canada. 571","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088012278"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.14552606,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"18","issue":"3","first_page":"571","last_page":"576"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9991999864578247,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9954000115394592,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8780851364135742},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8152000308036804},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.6700723171234131},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5061916708946228},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43195927143096924}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8780851364135742},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8152000308036804},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.6700723171234131},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5061916708946228},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43195927143096924}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895480100370797","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480100370797","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W122695541","https://openalex.org/W1029528332","https://openalex.org/W1965570465","https://openalex.org/W1997998268","https://openalex.org/W2017872859","https://openalex.org/W2031510973","https://openalex.org/W2045664805","https://openalex.org/W2049480048","https://openalex.org/W2074263179","https://openalex.org/W2081048040","https://openalex.org/W2082819223","https://openalex.org/W2095243185","https://openalex.org/W2951116413"],"related_works":["https://openalex.org/W4287020903","https://openalex.org/W2952259524","https://openalex.org/W2279732055","https://openalex.org/W2995857455","https://openalex.org/W2998840281","https://openalex.org/W2027277382","https://openalex.org/W4288805235","https://openalex.org/W1508013399","https://openalex.org/W3181135859","https://openalex.org/W4302399754"],"abstract_inverted_index":{"Let":[0],"${\\cal":[1,25,46,62],"F}$":[2,47,63],"be":[3],"a":[4,30,38,42,58,119,142,145,154,157],"family":[5],"of":[6,96,115,139,151],"graphs.":[7],"Two":[8],"graphs":[9,70],"G1":[10,49],"=":[11],"(V1":[12],",E1":[13],"),":[14],"G2":[15,65],"=(V2":[16],",E2":[17],")":[18],"are":[19],"said":[20],"to":[21,45,61],"have":[22,72],"the":[23,73,77,94,103,110],"same":[24,74,78],"F}$-structure":[26],"if":[27,50,53,88,91],"there":[28],"is":[29,86,114,122,141,153],"bijection":[31],"$f:":[32],"V_1":[33],"\\rightarrow":[34],"V_2$":[35],"such":[36],"that":[37,83],"subset":[39],"S":[40],"induces":[41,57],"graph":[43,59,84,99,120],"belonging":[44,60],"in":[48,64],"and":[51,89,108,124],"only":[52,90],"its":[54],"image":[55],"f(S)":[56],".":[66],"We":[67],"characterize":[68],"those":[69],"which":[71,113],"$\\{P_3,\\overline{P}_3\\}$-structure,":[75],"or":[76,135,144,147,156],"$\\{K_3,\\overline{K}_3\\}$-structure.":[79],"This":[80],"characterization":[81],"shows":[82],"H":[85],"perfect":[87,98],"it":[92],"has":[93,130],"$\\{P_3,\\overline{P}_3\\}$-structure":[95],"some":[97],"G.":[100],"In":[101],"proving":[102],"main":[104],"result,":[105,112],"we":[106],"need":[107],"prove":[109],"following":[111],"independent":[116],"interest:":[117],"If":[118],"J":[121,129,140],"claw-free":[123],"co-claw-free,":[125],"then":[126],"either":[127],"(i)":[128],"at":[131],"most":[132],"nine":[133],"vertices,":[134],"(ii)":[136],"every":[137,149],"component":[138,150],"path":[143,155],"hole,":[146],"(iii)":[148],"$\\overline{J}$":[152],"hole.":[158]},"counts_by_year":[{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}