{"id":"https://openalex.org/W2024931493","doi":"https://doi.org/10.1145/1374376.1374443","title":"Graph and map isomorphism and all polyhedral embeddings in linear time","display_name":"Graph and map isomorphism and all polyhedral embeddings in linear time","publication_year":2008,"publication_date":"2008-05-17","ids":{"openalex":"https://openalex.org/W2024931493","doi":"https://doi.org/10.1145/1374376.1374443","mag":"2024931493"},"language":"en","primary_location":{"id":"doi:10.1145/1374376.1374443","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1374376.1374443","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the fortieth annual ACM symposium on Theory of computing","raw_type":"proceedings-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/A5008961593","display_name":"Ken\u2010ichi Kawarabayashi","orcid":"https://orcid.org/0000-0001-6056-4287"},"institutions":[{"id":"https://openalex.org/I184597095","display_name":"National Institute of Informatics","ror":"https://ror.org/04ksd4g47","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I184597095","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Ken-ichi Kawarabayashi","raw_affiliation_strings":["National Institute of Informatics, Tokyo, Japan","(National Institute of Informatics, Tokyo, Japan)"],"affiliations":[{"raw_affiliation_string":"National Institute of Informatics, Tokyo, Japan","institution_ids":["https://openalex.org/I184597095"]},{"raw_affiliation_string":"(National Institute of Informatics, Tokyo, Japan)","institution_ids":["https://openalex.org/I184597095"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005993212","display_name":"Bojan Mohar","orcid":"https://orcid.org/0000-0002-7408-6148"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Bojan Mohar","raw_affiliation_strings":["Simon Fraser University, Burnaby, Canada","( Simon Fraser University Burnaby Canada )"],"affiliations":[{"raw_affiliation_string":"Simon Fraser University, Burnaby, Canada","institution_ids":["https://openalex.org/I18014758"]},{"raw_affiliation_string":"( Simon Fraser University Burnaby Canada )","institution_ids":["https://openalex.org/I18014758"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008961593"],"corresponding_institution_ids":["https://openalex.org/I184597095"],"apc_list":null,"apc_paid":null,"fwci":6.1644,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.96419541,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"471","last_page":"480"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9915000200271606,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/time-complexity","display_name":"Time complexity","score":0.6880645155906677},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6829587817192078},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6799454092979431},{"id":"https://openalex.org/keywords/graph-isomorphism","display_name":"Graph isomorphism","score":0.6493716835975647},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5748229622840881},{"id":"https://openalex.org/keywords/graph-embedding","display_name":"Graph embedding","score":0.5409319400787354},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4925547242164612},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.43722668290138245},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.39458638429641724},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17843300104141235},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.1671428680419922}],"concepts":[{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.6880645155906677},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6829587817192078},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6799454092979431},{"id":"https://openalex.org/C61665672","wikidata":"https://www.wikidata.org/wiki/Q303100","display_name":"Graph isomorphism","level":4,"score":0.6493716835975647},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5748229622840881},{"id":"https://openalex.org/C75564084","wikidata":"https://www.wikidata.org/wiki/Q5597085","display_name":"Graph embedding","level":3,"score":0.5409319400787354},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4925547242164612},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.43722668290138245},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.39458638429641724},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17843300104141235},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.1671428680419922},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1374376.1374443","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1374376.1374443","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the fortieth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.330.3538","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.330.3538","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.imfm.si/preprinti/PDF/01069.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":74,"referenced_works":["https://openalex.org/W132145278","https://openalex.org/W594463866","https://openalex.org/W1509664253","https://openalex.org/W1515854346","https://openalex.org/W1522210445","https://openalex.org/W1563039933","https://openalex.org/W1658031827","https://openalex.org/W1964700557","https://openalex.org/W1970795186","https://openalex.org/W1974672137","https://openalex.org/W1979774438","https://openalex.org/W1982180670","https://openalex.org/W1984897155","https://openalex.org/W1984976620","https://openalex.org/W1987374783","https://openalex.org/W1991755800","https://openalex.org/W1994556169","https://openalex.org/W2003311624","https://openalex.org/W2005079828","https://openalex.org/W2007513443","https://openalex.org/W2007578533","https://openalex.org/W2010203872","https://openalex.org/W2011112377","https://openalex.org/W2016588822","https://openalex.org/W2017024025","https://openalex.org/W2018099718","https://openalex.org/W2024420212","https://openalex.org/W2024491681","https://openalex.org/W2024935056","https://openalex.org/W2025685866","https://openalex.org/W2026005637","https://openalex.org/W2026943109","https://openalex.org/W2028348726","https://openalex.org/W2033336968","https://openalex.org/W2034485257","https://openalex.org/W2035409201","https://openalex.org/W2038643780","https://openalex.org/W2039714307","https://openalex.org/W2039732465","https://openalex.org/W2040404604","https://openalex.org/W2046021036","https://openalex.org/W2047577363","https://openalex.org/W2051748083","https://openalex.org/W2054639744","https://openalex.org/W2057826895","https://openalex.org/W2059372025","https://openalex.org/W2062337771","https://openalex.org/W2065139908","https://openalex.org/W2067016370","https://openalex.org/W2073558110","https://openalex.org/W2074411730","https://openalex.org/W2075516513","https://openalex.org/W2077202644","https://openalex.org/W2079325692","https://openalex.org/W2081812591","https://openalex.org/W2082687277","https://openalex.org/W2085348754","https://openalex.org/W2088455492","https://openalex.org/W2089527381","https://openalex.org/W2097289283","https://openalex.org/W2098626016","https://openalex.org/W2102151147","https://openalex.org/W2108471507","https://openalex.org/W2113363067","https://openalex.org/W2120446949","https://openalex.org/W2148957455","https://openalex.org/W2159366821","https://openalex.org/W2161714963","https://openalex.org/W2165303918","https://openalex.org/W2744383773","https://openalex.org/W2798588639","https://openalex.org/W3202159599","https://openalex.org/W4319589071","https://openalex.org/W6742212607"],"related_works":["https://openalex.org/W2109056537","https://openalex.org/W1798304401","https://openalex.org/W2476624396","https://openalex.org/W4302177579","https://openalex.org/W3036264823","https://openalex.org/W4383180681","https://openalex.org/W3206528106","https://openalex.org/W2123605750","https://openalex.org/W2912814903","https://openalex.org/W2082479932"],"abstract_inverted_index":{"For":[0],"every":[1],"surface":[2,152,201],"S":[3,103,127],"(orientable":[4],"or":[5,133],"non-orientable),":[6],"we":[7,118,212],"give":[8,165,213],"a":[9,36,86,105,109,214,218,241],"linear":[10,79,242,268],"time":[11,41,65,80,243,269],"algorithm":[12,39,56,163,244],"to":[13,120,174],"test":[14],"the":[15,48,54,59,64,99,151,162,178,186,200,203,206,209,222,229,254],"graph":[16,110,183,262],"isomorphism":[17,247,263],"of":[18,22,27,50,61,83,90,95,124,128,168,180,189,191,208,231,234,257],"two":[19,78],"graphs,":[20],"one":[21],"which":[23,58,84,194],"admits":[24],"an":[25,113,122,137,160,181],"embedding":[26,123,138],"face-width":[28,129,169,179],"at":[29,130,170],"least":[30,131,171],"3":[31],"into":[32],"S.":[33,51],"This":[34,52,251],"improves":[35],"previously":[37],"known":[38,144],"whose":[40],"complexity":[42,66],"is":[43,47,53,75,89,98,143,148,153,159,185,240],"nO(g),":[44],"where":[45],"g":[46],"genus":[49],"first":[55,94],"for":[57,221,245,270],"degree":[60],"polynomial":[62],"in":[63,126,193,199,267],"does":[67,139],"not":[68,140,154],"depend":[69],"on":[70,77],"g.":[71],"The":[72,93,237],"above":[73,210],"result":[74,256],"based":[76],"algorithms,":[81],"each":[82],"solves":[85],"problem":[87,147],"that":[88,135,145,261],"independent":[91],"interest.":[92],"these":[96],"problems":[97],"following":[100],"one.":[101],"Let":[102],"be":[104,265],"fixed":[106],"surface.":[107],"Given":[108],"G":[111,125,184,192],"and":[112,217,226,248,259],"integer":[114],"k":[115],"\u2265":[116],"3,":[117],"want":[119],"find":[121],"k,":[132,172],"conclude":[134],"such":[136],"exist.":[141],"It":[142],"this":[146],"NP-hard":[149],"when":[150],"fixed.":[155],"Moreover,":[156],"if":[157],"there":[158],"embedding,":[161],"can":[164,264],"all":[166],"embeddings":[167,233],"up":[173],"Whitney":[175,249],"equivalence.":[176,250],"Here,":[177],"embedded":[182],"minimum":[187],"number":[188,230],"points":[190],"some":[195],"non-contractible":[196],"closed":[197],"curve":[198],"intersects":[202],"graph.":[204],"In":[205],"proof":[207,216],"algorithm,":[211],"simpler":[215],"better":[219],"bound":[220],"theorem":[223],"by":[224],"Mohar":[225],"Robertson":[227],"concerning":[228],"polyhedral":[232],"3-connected":[235],"graphs.":[236,272],"second":[238],"ingredient":[239],"map":[246],"part":[252],"generalizes":[253],"seminal":[255],"Hopcroft":[258],"Wong":[260],"decided":[266],"planar":[271]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}