{"id":"https://openalex.org/W2086459036","doi":"https://doi.org/10.1016/s0012-365x(01)00463-0","title":"Plane triangulations are 6-partitionable","display_name":"Plane triangulations are 6-partitionable","publication_year":2002,"publication_date":"2002-09-01","ids":{"openalex":"https://openalex.org/W2086459036","doi":"https://doi.org/10.1016/s0012-365x(01)00463-0","mag":"2086459036"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(01)00463-0","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5041941673","display_name":"Ajit A. Diwan","orcid":"https://orcid.org/0000-0001-9381-7164"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Ajit A. Diwan","raw_affiliation_strings":["Department of Computer Science and Engineering, Indian Institute of Technology, Bombay, Mumbai 400076, India"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Indian Institute of Technology, Bombay, Mumbai 400076, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065764073","display_name":"Manish Kurhekar","orcid":"https://orcid.org/0000-0002-6409-3280"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Manish P. Kurhekar","raw_affiliation_strings":["Department of Computer Science and Engineering, Indian Institute of Technology, Bombay, Mumbai 400076, India"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Indian Institute of Technology, Bombay, Mumbai 400076, India","institution_ids":["https://openalex.org/I162827531"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041941673"],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000,"provenance":"doaj"},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":4,"citation_normalized_percentile":{"value":0.601216,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":71,"max":73},"biblio":{"volume":"256","issue":"1-2","first_page":"91","last_page":"103"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9997,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9997,"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/T10374","display_name":"Graph Theory and Algorithms","score":0.9879,"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":"Optical Code Division Multiple Access","score":0.9854,"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/graph-partition","display_name":"Graph partition","score":0.48553252},{"id":"https://openalex.org/keywords/graph-labeling","display_name":"Graph Labeling","score":0.48506}],"concepts":[{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.8113482},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8087653},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.78503287},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6054785},{"id":"https://openalex.org/C48903430","wikidata":"https://www.wikidata.org/wiki/Q491370","display_name":"Graph partition","level":3,"score":0.48553252},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.46376252},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4112739}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(01)00463-0","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":5,"referenced_works":["https://openalex.org/W1970776799","https://openalex.org/W1983999399","https://openalex.org/W1997165382","https://openalex.org/W2050065904","https://openalex.org/W2083409154"],"related_works":["https://openalex.org/W4301046126","https://openalex.org/W3183075326","https://openalex.org/W3173312668","https://openalex.org/W3139829055","https://openalex.org/W3134869969","https://openalex.org/W3012931947","https://openalex.org/W2810695303","https://openalex.org/W2782513589","https://openalex.org/W2583811263","https://openalex.org/W2035944803"],"abstract_inverted_index":{"Given":[0],"a":[1,16,30,39,43,61],"graph":[2,48],"G=(V,E)":[3],"and":[4,27],"k":[5,71],"positive":[6],"integers":[7],"n1,n2,\u2026,nk":[8],"such":[9,24],"that":[10,25,83,93],"\u2211i=1kni=|V|,":[11],"we":[12,91],"wish":[13],"to":[14,55],"find":[15],"partition":[17,40,67],"P1,P2,\u2026,Pk":[18],"of":[19,33,45,63,68],"the":[20,101],"vertex":[21],"set":[22],"V":[23],"|Pi|=ni":[26],"Pi":[28],"induces":[29],"connected":[31],"subgraph":[32],"G":[34,49,64],"for":[35,65],"all":[36],"i,1\u2a7di\u2a7dk.":[37],"Such":[38],"is":[41,53,100],"called":[42],"k-partition":[44,62],"G.":[46],"A":[47],"with":[50],"n":[51,69],"vertices":[52],"said":[54],"be":[56],"k-partitionable":[57],"if":[58],"there":[59,105],"exists":[60],"any":[66],"into":[70],"parts.":[72],"Lov\u00e1sz":[73],"(Acta":[74],"Math.":[75],"Acad.":[76],"Sci.":[77],"Hungar.":[78],"30":[79],"(1977)":[80],"241)":[81],"showed":[82],"k-connected":[84],"graphs":[85],"are":[86,96,110],"k-partitionable.":[87],"In":[88],"this":[89],"paper":[90],"prove":[92],"plane":[94,107],"triangulations":[95,108],"6-partitionable.":[97],"This":[98],"result":[99],"best":[102],"possible":[103],"as":[104],"exist":[106],"which":[109],"not":[111],"7-partitionable.":[112]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2086459036","counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2024-09-25T03:40:53.581195","created_date":"2016-06-24"}
