{"id":"https://openalex.org/W3048268335","doi":"https://doi.org/10.1007/s00453-020-00747-x","title":"Graph Isomorphism for $$(H_1,H_2)$$-Free Graphs: An\u00a0Almost Complete Dichotomy","display_name":"Graph Isomorphism for $$(H_1,H_2)$$-Free Graphs: An\u00a0Almost Complete Dichotomy","publication_year":2020,"publication_date":"2020-08-05","ids":{"openalex":"https://openalex.org/W3048268335","doi":"https://doi.org/10.1007/s00453-020-00747-x","mag":"3048268335"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-020-00747-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-020-00747-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-020-00747-x.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-020-00747-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029166445","display_name":"Marthe Bonamy","orcid":"https://orcid.org/0000-0001-7905-8018"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Marthe Bonamy","raw_affiliation_strings":["CNRS, LaBRI, Universit\u00e9 de Bordeaux, Bordeaux, France"],"affiliations":[{"raw_affiliation_string":"CNRS, LaBRI, Universit\u00e9 de Bordeaux, Bordeaux, France","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210160189","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044190443","display_name":"Nicol\u00e1s Bousquet","orcid":"https://orcid.org/0000-0003-0170-0503"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210155607","display_name":"Laboratoire d'Informatique en Images et Syst\u00e8mes d'Information","ror":"https://ror.org/04dv4he91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I188626449","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210155607","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Bousquet","raw_affiliation_strings":["CNRS, LIRIS, Univ. Lyon, Universit\u00e9 Lyon 1, Villeurbanne, France"],"affiliations":[{"raw_affiliation_string":"CNRS, LIRIS, Univ. Lyon, Universit\u00e9 Lyon 1, Villeurbanne, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I4210155607","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085663992","display_name":"Konrad K. Dabrowski","orcid":"https://orcid.org/0000-0001-9515-6945"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Konrad K. Dabrowski","raw_affiliation_strings":["Department of Computer Science, Durham University, Durham, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Durham University, Durham, UK","institution_ids":["https://openalex.org/I190082696"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029365650","display_name":"Matthew Johnson","orcid":"https://orcid.org/0000-0002-7295-2663"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Matthew Johnson","raw_affiliation_strings":["Department of Computer Science, Durham University, Durham, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Durham University, Durham, UK","institution_ids":["https://openalex.org/I190082696"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027487467","display_name":"Dani\u00ebl Paulusma","orcid":"https://orcid.org/0000-0001-5945-9287"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Dani\u00ebl Paulusma","raw_affiliation_strings":["Department of Computer Science, Durham University, Durham, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Durham University, Durham, UK","institution_ids":["https://openalex.org/I190082696"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089101660","display_name":"Th\u00e9o Pierron","orcid":"https://orcid.org/0000-0002-5586-5613"},"institutions":[{"id":"https://openalex.org/I21449261","display_name":"Masaryk University","ror":"https://ror.org/02j46qs45","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21449261"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Th\u00e9o Pierron","raw_affiliation_strings":["Faculty of Informatics, Masaryk University, Botanick\u00e1 68A, 602 00, Brno, Czech Republic","Faculty of Informatics, Masaryk University, Brno, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Faculty of Informatics, Masaryk University, Botanick\u00e1 68A, 602 00, Brno, Czech Republic","institution_ids":["https://openalex.org/I21449261"]},{"raw_affiliation_string":"Faculty of Informatics, Masaryk University, Brno, Czech Republic","institution_ids":["https://openalex.org/I21449261"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5085663992"],"corresponding_institution_ids":["https://openalex.org/I190082696"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.4335,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69182181,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"83","issue":"3","first_page":"822","last_page":"852"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9980000257492065,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9922000169754028,"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/algorithm","display_name":"Algorithm","score":0.6045500636100769},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42087990045547485},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33102405071258545}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6045500636100769},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42087990045547485},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33102405071258545}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00453-020-00747-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-020-00747-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-020-00747-x.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:dro.dur.ac.uk.OAI2:31257","is_oa":true,"landing_page_url":"http://dro.dur.ac.uk/31257/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196258","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Algorithmica, 2021, Vol.83(3), pp.822-852 [Peer Reviewed Journal]","raw_type":"Article"},{"id":"pmh:oai:HAL:hal-03394356v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03394356","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithmica, 2021, 83 (3), pp.822-852. &#x27E8;10.1007/s00453-020-00747-x&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:durham-repository.worktribe.com:1266628","is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/output/1266628","pdf_url":null,"source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s00453-020-00747-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-020-00747-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-020-00747-x.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1199503345","display_name":null,"funder_award_id":"ANR-18-CE40-0032","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G1376760675","display_name":null,"funder_award_id":"EP/K025090/1","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G1508931271","display_name":"Detecting Induced Graph Patterns","funder_award_id":"EP/K025090/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1692876670","display_name":null,"funder_award_id":"ANR-17-CE40-0022","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G1857028073","display_name":null,"funder_award_id":"RPG-2016-258","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4038043572","display_name":null,"funder_award_id":"MUNI Award in Science and Humanities","funder_id":"https://openalex.org/F4320326548","funder_display_name":"Masarykova Univerzita"},{"id":"https://openalex.org/G410877973","display_name":null,"funder_award_id":"EP/K025090","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4770415168","display_name":null,"funder_award_id":"SC7-1718-04","funder_id":"https://openalex.org/F4320320184","funder_display_name":"London Mathematical Society"},{"id":"https://openalex.org/G51464283","display_name":null,"funder_award_id":"RPG-2016-258","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G6191833929","display_name":null,"funder_award_id":"EP/K025090/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6803667113","display_name":null,"funder_award_id":"ANR-17","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6851345361","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6876561401","display_name":null,"funder_award_id":"ANR-18","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320320184","display_name":"London Mathematical Society","ror":"https://ror.org/01r1e1h27"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320326548","display_name":"Masarykova Univerzita","ror":"https://ror.org/02j46qs45"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3048268335.pdf","grobid_xml":"https://content.openalex.org/works/W3048268335.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W94262720","https://openalex.org/W1511942180","https://openalex.org/W1663329006","https://openalex.org/W1706559987","https://openalex.org/W1967307108","https://openalex.org/W1974672137","https://openalex.org/W1991005941","https://openalex.org/W1994331970","https://openalex.org/W1998244133","https://openalex.org/W2018099718","https://openalex.org/W2097725094","https://openalex.org/W2111070448","https://openalex.org/W2116334057","https://openalex.org/W2162763810","https://openalex.org/W2280002837","https://openalex.org/W2409645877","https://openalex.org/W2559777123","https://openalex.org/W2593190625","https://openalex.org/W2598883699","https://openalex.org/W2620375528","https://openalex.org/W2623827933","https://openalex.org/W2763059940","https://openalex.org/W2796422101","https://openalex.org/W2949284609","https://openalex.org/W2963233231","https://openalex.org/W2963366865","https://openalex.org/W2963640883","https://openalex.org/W2963678182","https://openalex.org/W2964662878","https://openalex.org/W2966381141","https://openalex.org/W3004925707"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"resolve":[2],"the":[3,66,76,118],"computational":[4],"complexity":[5],"of":[6,11,68,92,120,125],"Graph":[7,84,111],"Isomorphism":[8,85,112],"for":[9,38,123,127],"classes":[10,91],"graphs":[12,146],"characterized":[13],"by":[14],"two":[15],"forbidden":[16],"induced":[17],"subgraphs":[18],"$$":[19,21],"H_{1}":[20],"<mml:math":[22,31,44,129],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[23,32,45,130],"<mml:msub>":[24,33,48,53,133,138],"<mml:mi>H</mml:mi>":[25,34,49,54,134,139],"<mml:mn>1</mml:mn>":[26,50,135],"</mml:msub>":[27,36,51,56,136,141],"</mml:math>":[28,37,59,144],"and":[29,80,113],"$$H_2$$":[30],"<mml:mn>2</mml:mn>":[35,55,140],"all":[39],"but":[40,73],"six":[41],"pairs":[42],"$$(H_1,H_2)$$":[43,128],"<mml:mrow>":[46,131],"<mml:mo>(</mml:mo>":[47,132],"<mml:mo>,</mml:mo>":[52,137],"<mml:mo>)</mml:mo>":[57,142],"</mml:mrow>":[58,143],".":[60],"Schweitzer":[61,81],"had":[62],"previously":[63],"shown":[64],"that":[65,83],"number":[67,119],"open":[69,77,121],"cases":[70,122],"was":[71],"finite,":[72],"without":[74],"specifying":[75],"cases.":[78],"Grohe":[79],"proved":[82],"is":[86],"polynomial-time":[87],"solvable":[88],"on":[89],"graph":[90],"bounded":[93],"clique-width.":[94],"Our":[95],"work":[96],"combines":[97],"known":[98],"results":[99],"such":[100],"as":[101],"these":[102],"with":[103],"new":[104],"results.":[105],"By":[106],"exploiting":[107],"a":[108],"relationship":[109],"between":[110],"clique-width,":[114],"we":[115],"simultaneously":[116],"reduce":[117],"boundedness":[124],"clique-width":[126],"-free":[145],"to":[147],"five.":[148]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}