{"id":"https://openalex.org/W2012357906","doi":"https://doi.org/10.1137/0402004","title":"Graph Bipartization and via minimization","display_name":"Graph Bipartization and via minimization","publication_year":1989,"publication_date":"1989-02-01","ids":{"openalex":"https://openalex.org/W2012357906","doi":"https://doi.org/10.1137/0402004","mag":"2012357906"},"language":"en","primary_location":{"id":"doi:10.1137/0402004","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0402004","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/A5103910452","display_name":"Hyeong\u2010Ah Choi","orcid":null},"institutions":[{"id":"https://openalex.org/I193531525","display_name":"George Washington University","ror":"https://ror.org/00y4zzh67","country_code":"US","type":"education","lineage":["https://openalex.org/I193531525"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hyeong-Ah Choi","raw_affiliation_strings":["George Washington University  Washington, DC"],"affiliations":[{"raw_affiliation_string":"George Washington University  Washington, DC","institution_ids":["https://openalex.org/I193531525"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102116980","display_name":"Kazuo Nakajima","orcid":null},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kazuo Nakajima","raw_affiliation_strings":["University of Maryland, College Park"],"affiliations":[{"raw_affiliation_string":"University of Maryland, College Park","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077534374","display_name":"C.S. Rim","orcid":null},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chong S. Rim","raw_affiliation_strings":["University of Maryland, College Park"],"affiliations":[{"raw_affiliation_string":"University of Maryland, College Park","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103910452"],"corresponding_institution_ids":["https://openalex.org/I193531525"],"apc_list":null,"apc_paid":null,"fwci":0.84672606,"has_fulltext":false,"cited_by_count":66,"citation_normalized_percentile":{"value":0.73610033,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"2","issue":"1","first_page":"38","last_page":"47"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9998999834060669,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9998999834060669,"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/T11032","display_name":"VLSI and Analog Circuit Testing","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9969000220298767,"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":0.8135330677032471},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6822181940078735},{"id":"https://openalex.org/keywords/neighbourhood","display_name":"Neighbourhood (mathematics)","score":0.6537014245986938},{"id":"https://openalex.org/keywords/feedback-vertex-set","display_name":"Feedback vertex set","score":0.6263987421989441},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5352632999420166},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4920811057090759},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.49076923727989197},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.4456251859664917},{"id":"https://openalex.org/keywords/regular-graph","display_name":"Regular graph","score":0.44516512751579285},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.410347580909729},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.374600350856781},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3717638850212097}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8135330677032471},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6822181940078735},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.6537014245986938},{"id":"https://openalex.org/C28723256","wikidata":"https://www.wikidata.org/wiki/Q1400918","display_name":"Feedback vertex set","level":4,"score":0.6263987421989441},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5352632999420166},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4920811057090759},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.49076923727989197},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.4456251859664917},{"id":"https://openalex.org/C123482549","wikidata":"https://www.wikidata.org/wiki/Q826467","display_name":"Regular graph","level":5,"score":0.44516512751579285},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.410347580909729},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.374600350856781},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3717638850212097},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0402004","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0402004","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":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1519644264","https://openalex.org/W1964700557","https://openalex.org/W1965921519","https://openalex.org/W2012931553","https://openalex.org/W2020112047","https://openalex.org/W2030087828","https://openalex.org/W2045027193","https://openalex.org/W2066577300","https://openalex.org/W2073705438","https://openalex.org/W2141923701"],"related_works":["https://openalex.org/W2021104046","https://openalex.org/W782850337","https://openalex.org/W3104325023","https://openalex.org/W4319599984","https://openalex.org/W3205099810","https://openalex.org/W3100313843","https://openalex.org/W3105144174","https://openalex.org/W3104688290","https://openalex.org/W2045919248","https://openalex.org/W2044101286"],"abstract_inverted_index":{"The":[0],"vertex-":[1],"(respectively,":[2,17],"edge-)":[3],"deletion":[4],"graph":[5,21,28,37,54,81,94,121],"bipartization":[6,38,55,82,95,122],"problem":[7,10,39,56,83,96,123],"is":[8,70,84,97,110,115,124,140,160,168],"the":[9,26,35,52,66,79,91,106,119,130,144,151,164],"of":[11,15,43,60,153],"deleting":[12],"a":[13,20,41,58],"set":[14],"vertices":[16],"edges)":[18],"from":[19],"so":[22],"as":[23],"to":[24,72,112,170],"make":[25],"remaining":[27],"bipartite.":[29],"This":[30,74],"paper":[31],"first":[32],"shows":[33],"that":[34,77,118,143],"vertex-deletion":[36,80,93,120],"has":[40,57],"solution":[42,59],"size":[44,61],"k":[45,62],"or":[46,63],"less":[47],"if":[48,51],"and":[49,89,156],"only":[50],"edge-deletion":[53],"less,":[64],"when":[65,105,129,163],"maximum":[67,107,131,165],"vertex":[68,108,132],"degree":[69,109,133,167],"limited":[71,111,169],"three.":[73,113,135],"immediately":[75],"implies":[76],"(1)":[78],"NP-complete":[85,125,161],"for":[86,102,126],"cubic":[87],"graphs,":[88],"(2)":[90],"minimum":[92],"solvable":[98],"in":[99,150],"polynomial":[100],"time":[101],"planar":[103,127],"graphs":[104,128],"It":[114],"then":[116],"proved":[117],"exceeds":[134],"Using":[136],"this":[137],"result,":[138],"it":[139],"finally":[141],"shown":[142],"via":[145],"minimization":[146],"problem,":[147],"which":[148],"arises":[149],"design":[152],"integrated":[154],"circuits":[155],"printed":[157],"circuit":[158],"boards,":[159],"even":[162],"\"junction\"":[166],"four.":[171]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-02-15T07:36:51.736424","created_date":"2025-10-10T00:00:00"}