{"id":"https://openalex.org/W4417307720","doi":"https://doi.org/10.2197/ipsjjip.33.1033","title":"An Upper Bound for the Permutation-representation Number of Bipartite Graphs","display_name":"An Upper Bound for the Permutation-representation Number of Bipartite Graphs","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4417307720","doi":"https://doi.org/10.2197/ipsjjip.33.1033"},"language":"en","primary_location":{"id":"doi:10.2197/ipsjjip.33.1033","is_oa":true,"landing_page_url":"https://doi.org/10.2197/ipsjjip.33.1033","pdf_url":"https://www.jstage.jst.go.jp/article/ipsjjip/33/0/33_1033/_pdf","source":{"id":"https://openalex.org/S4210239267","display_name":"Journal of Information Processing","issn_l":"1882-6652","issn":["1882-6652"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Information Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.jstage.jst.go.jp/article/ipsjjip/33/0/33_1033/_pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084605257","display_name":"Khyodeno Mozhui","orcid":"https://orcid.org/0009-0009-3711-2827"},"institutions":[{"id":"https://openalex.org/I1317621060","display_name":"Indian Institute of Technology Guwahati","ror":"https://ror.org/0022nd079","country_code":"IN","type":"education","lineage":["https://openalex.org/I1317621060"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Khyodeno Mozhui","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Guwahati"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Guwahati","institution_ids":["https://openalex.org/I1317621060"]}]},{"author_position":"last","author":{"id":null,"display_name":"Kanduru Venkata Krishna","orcid":null},"institutions":[{"id":"https://openalex.org/I1317621060","display_name":"Indian Institute of Technology Guwahati","ror":"https://ror.org/0022nd079","country_code":"IN","type":"education","lineage":["https://openalex.org/I1317621060"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kanduru Venkata Krishna","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Guwahati"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Guwahati","institution_ids":["https://openalex.org/I1317621060"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5084605257"],"corresponding_institution_ids":["https://openalex.org/I1317621060"],"apc_list":null,"apc_paid":null,"fwci":1.348,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.87594272,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"33","issue":"0","first_page":"1033","last_page":"1041"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.5256999731063843,"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":0.5256999731063843,"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":0.27869999408721924,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.03840000182390213,"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/bipartite-graph","display_name":"Bipartite graph","score":0.7436000108718872},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.47049999237060547},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.4569000005722046},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4472000002861023},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4465000033378601},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.40209999680519104},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.365200012922287},{"id":"https://openalex.org/keywords/cograph","display_name":"Cograph","score":0.3540000021457672}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7940000295639038},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7436000108718872},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5656999945640564},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5002999901771545},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.47049999237060547},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.4569000005722046},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4472000002861023},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4465000033378601},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.40209999680519104},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.365200012922287},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.3540000021457672},{"id":"https://openalex.org/C200597783","wikidata":"https://www.wikidata.org/wiki/Q4391289","display_name":"Edge-transitive graph","level":5,"score":0.3273000121116638},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31200000643730164},{"id":"https://openalex.org/C198414033","wikidata":"https://www.wikidata.org/wiki/Q5155607","display_name":"Comparability graph","level":5,"score":0.2922999858856201},{"id":"https://openalex.org/C123482549","wikidata":"https://www.wikidata.org/wiki/Q826467","display_name":"Regular graph","level":5,"score":0.29179999232292175},{"id":"https://openalex.org/C168291704","wikidata":"https://www.wikidata.org/wiki/Q902252","display_name":"Complement graph","level":5,"score":0.28949999809265137},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.28519999980926514},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2824000120162964},{"id":"https://openalex.org/C113203676","wikidata":"https://www.wikidata.org/wiki/Q220997","display_name":"Vertex-transitive graph","level":5,"score":0.2757999897003174}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2197/ipsjjip.33.1033","is_oa":true,"landing_page_url":"https://doi.org/10.2197/ipsjjip.33.1033","pdf_url":"https://www.jstage.jst.go.jp/article/ipsjjip/33/0/33_1033/_pdf","source":{"id":"https://openalex.org/S4210239267","display_name":"Journal of Information Processing","issn_l":"1882-6652","issn":["1882-6652"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Information Processing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.2197/ipsjjip.33.1033","is_oa":true,"landing_page_url":"https://doi.org/10.2197/ipsjjip.33.1033","pdf_url":"https://www.jstage.jst.go.jp/article/ipsjjip/33/0/33_1033/_pdf","source":{"id":"https://openalex.org/S4210239267","display_name":"Journal of Information Processing","issn_l":"1882-6652","issn":["1882-6652"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Information Processing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320327457","display_name":"Indian Institute of Technology Guwahati","ror":"https://ror.org/0022nd079"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4417307720.pdf","grobid_xml":"https://content.openalex.org/works/W4417307720.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1767557960","https://openalex.org/W1956452579","https://openalex.org/W1974972093","https://openalex.org/W1985734960","https://openalex.org/W1987554952","https://openalex.org/W2021339822","https://openalex.org/W2036163012","https://openalex.org/W2047899424","https://openalex.org/W2065003891","https://openalex.org/W2069161802","https://openalex.org/W2074390982","https://openalex.org/W2076908141","https://openalex.org/W2093031769","https://openalex.org/W2136112991","https://openalex.org/W2154635726","https://openalex.org/W2157529519","https://openalex.org/W2269342346","https://openalex.org/W2325654786","https://openalex.org/W2748096547","https://openalex.org/W2911323838","https://openalex.org/W2963296039","https://openalex.org/W2963499318","https://openalex.org/W2963886547","https://openalex.org/W4251134381","https://openalex.org/W4254807835"],"related_works":[],"abstract_inverted_index":{"A":[0,45],"word-representable":[1,46,76],"graph":[2,7,47,80,101,158,184,236],"G=(V,E)":[3],"is":[4,69,81,93,102,111,185],"a":[5,13,26,37,52,79,84,94,156,182,224,229,233],"simple":[6],"which":[8,55],"can":[9,48],"be":[10,49],"represented":[11,50,82],"by":[12,51,83],"word":[14,43,53,85,230],"w":[15],"over":[16],"its":[17,97,163],"vertex":[18],"set":[19],"V":[20],"such":[21,67,109],"that":[22,168,177,231],"any":[23],"two":[24],"vertices":[25],"and":[27,34,38,106,130,159,166,199,202,238],"b":[28,39],"of":[29,74,86,96,119,138,155,162,181,196,207,248],"G":[30],"are":[31],"adjacent":[32],"if":[33,36],"only":[35],"alternate":[40],"in":[41,54],"the":[42,65,71,75,87,100,107,113,120,125,127,131,146,150,153,160,171,179,194,205,246],"w.":[44],"each":[56,91],"letter":[57],"appears":[58],"exactly":[59],"k":[60,68,110],"times,":[61],"for":[62,135,245],"some":[63],"k;":[64],"smallest":[66,108],"called":[70,103,112],"representation":[72,128],"number":[73,115,129],"graph.":[77,123],"If":[78],"form":[88],"p1p2\u2026pk":[89],"where":[90],"pi":[92],"permutation":[95],"vertices,":[98],"then":[99],"permutationally":[104,121],"representable,":[105],"permutation-representation":[114],"(in":[116],"short,":[117],"prn)":[118],"representable":[122],"In":[124,141],"literature,":[126],"prn":[132,154,180,195,206,247],"were":[133],"established":[134],"certain":[136],"subclasses":[137],"bipartite":[139,183,200,208,235,249],"graphs.":[140,219,250],"this":[142],"work,":[143],"focusing":[144],"on":[145,193],"prn,":[147],"we":[148,175,188,213,221],"observe":[149],"relation":[151],"between":[152],"comparability":[157,197],"dimension":[161],"induced":[164],"poset,":[165],"note":[167],"they":[169],"have":[170],"same":[172],"value.":[173],"Accordingly,":[174],"ascertain":[176],"determining":[178],"NP-hard.":[186],"Next,":[187],"review":[189],"existing":[190],"upper":[191,243],"bounds":[192],"graphs":[198,209],"graphs,":[201],"subsequently":[203],"examine":[204],"using":[210],"specific":[211],"constructions":[212],"refer":[214],"to":[215,227],"as":[216],"neighborhood":[217],"inclusion":[218],"Here,":[220],"both":[222],"devise":[223],"polynomial-time":[225],"procedure":[226],"construct":[228],"represents":[232],"given":[234],"permutationally,":[237],"also":[239],"provide":[240],"an":[241],"improved":[242],"bound":[244]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-12-14T00:00:00"}