{"id":"https://openalex.org/W2015142920","doi":"https://doi.org/10.1137/070687256","title":"Clique-Width is NP-Complete","display_name":"Clique-Width is NP-Complete","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2015142920","doi":"https://doi.org/10.1137/070687256","mag":"2015142920"},"language":"en","primary_location":{"id":"doi:10.1137/070687256","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070687256","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/A5054676766","display_name":"Michael R. Fellows","orcid":"https://orcid.org/0000-0002-6148-9212"},"institutions":[{"id":"https://openalex.org/I2800844553","display_name":"Newcastle College","ror":"https://ror.org/04jmcwc90","country_code":"GB","type":"education","lineage":["https://openalex.org/I2800844553"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Michael R. Fellows","raw_affiliation_strings":["michael.fellows@newcastle.edu.au and frances.rosamond@newcastle.edu.au#TAB#"],"affiliations":[{"raw_affiliation_string":"michael.fellows@newcastle.edu.au and frances.rosamond@newcastle.edu.au#TAB#","institution_ids":["https://openalex.org/I2800844553"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047322831","display_name":"Frances Rosamond","orcid":"https://orcid.org/0000-0002-5097-9929"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Frances A. Rosamond","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069504394","display_name":"Udi Rotics","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Udi Rotics","raw_affiliation_strings":["rotics@mars.netanya.ac.il#TAB#"],"affiliations":[{"raw_affiliation_string":"rotics@mars.netanya.ac.il#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037092803","display_name":"Stefan Szeider","orcid":"https://orcid.org/0000-0001-8994-1656"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefan Szeider","raw_affiliation_strings":["stefan.szeider@durham.ac.uk#TAB#"],"affiliations":[{"raw_affiliation_string":"stefan.szeider@durham.ac.uk#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5054676766"],"corresponding_institution_ids":["https://openalex.org/I2800844553"],"apc_list":null,"apc_paid":null,"fwci":6.0095,"has_fulltext":false,"cited_by_count":114,"citation_normalized_percentile":{"value":0.9652351,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"23","issue":"2","first_page":"909","last_page":"939"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":1.0,"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":1.0,"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":0.9984999895095825,"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":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8289452791213989},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7788299322128296},{"id":"https://openalex.org/keywords/split-graph","display_name":"Split graph","score":0.5667626261711121},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5652375817298889},{"id":"https://openalex.org/keywords/clique-graph","display_name":"Clique graph","score":0.5650376677513123},{"id":"https://openalex.org/keywords/clique-width","display_name":"Clique-width","score":0.4867684841156006},{"id":"https://openalex.org/keywords/perfect-graph","display_name":"Perfect graph","score":0.48586505651474},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4824974536895752},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4753289520740509},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.4704899787902832},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4647236466407776},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4452190399169922},{"id":"https://openalex.org/keywords/block-graph","display_name":"Block graph","score":0.41368046402931213},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.4101966619491577},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.34692323207855225},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.21490216255187988},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.21415454149246216},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.1957794427871704},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.14499127864837646},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.09778675436973572}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8289452791213989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7788299322128296},{"id":"https://openalex.org/C8554925","wikidata":"https://www.wikidata.org/wiki/Q3893853","display_name":"Split graph","level":5,"score":0.5667626261711121},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5652375817298889},{"id":"https://openalex.org/C189239283","wikidata":"https://www.wikidata.org/wiki/Q17101022","display_name":"Clique graph","level":5,"score":0.5650376677513123},{"id":"https://openalex.org/C5737132","wikidata":"https://www.wikidata.org/wiki/Q1101814","display_name":"Clique-width","level":5,"score":0.4867684841156006},{"id":"https://openalex.org/C32972407","wikidata":"https://www.wikidata.org/wiki/Q1187620","display_name":"Perfect graph","level":5,"score":0.48586505651474},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4824974536895752},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4753289520740509},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.4704899787902832},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4647236466407776},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4452190399169922},{"id":"https://openalex.org/C43413943","wikidata":"https://www.wikidata.org/wiki/Q4927193","display_name":"Block graph","level":5,"score":0.41368046402931213},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.4101966619491577},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.34692323207855225},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.21490216255187988},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.21415454149246216},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.1957794427871704},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.14499127864837646},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.09778675436973572},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/070687256","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070687256","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"},{"id":"pmh:oai:espace.cdu.edu.au:cdu:9771","is_oa":false,"landing_page_url":"http://espace.cdu.edu.au/view/cdu:9771","pdf_url":null,"source":{"id":"https://openalex.org/S4306401536","display_name":"CDU eSpace Institutional Repository (Charles Darwin University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I29894533","host_organization_name":"Charles Darwin University","host_organization_lineage":["https://openalex.org/I29894533"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","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":29,"referenced_works":["https://openalex.org/W182638888","https://openalex.org/W1558330704","https://openalex.org/W1560032421","https://openalex.org/W1993328543","https://openalex.org/W1994331970","https://openalex.org/W1994887153","https://openalex.org/W2013967419","https://openalex.org/W2022499468","https://openalex.org/W2026616451","https://openalex.org/W2027562075","https://openalex.org/W2029001691","https://openalex.org/W2035344492","https://openalex.org/W2046616287","https://openalex.org/W2052867211","https://openalex.org/W2053991811","https://openalex.org/W2063063505","https://openalex.org/W2063132075","https://openalex.org/W2063291872","https://openalex.org/W2063951771","https://openalex.org/W2070790034","https://openalex.org/W2076819776","https://openalex.org/W2085550081","https://openalex.org/W2087911394","https://openalex.org/W2101392634","https://openalex.org/W2109121075","https://openalex.org/W2109716789","https://openalex.org/W2112067601","https://openalex.org/W2126513401","https://openalex.org/W2171507355"],"related_works":["https://openalex.org/W2079220110","https://openalex.org/W2936075899","https://openalex.org/W2186006531","https://openalex.org/W1614693244","https://openalex.org/W4315881088","https://openalex.org/W2179401580","https://openalex.org/W2067182946","https://openalex.org/W3003390052","https://openalex.org/W1523717587","https://openalex.org/W2015142920"],"abstract_inverted_index":{"Clique-width":[0],"is":[1,88,92],"a":[2,8,14,56,75,96],"graph":[3,17,58,76],"parameter":[4],"that":[5,52,98],"measures":[6],"in":[7,22,42,63,107],"certain":[9],"sense":[10],"the":[11,53,84,103,108],"complexity":[12],"of":[13,47,55,86,105],"graph.":[15],"Hard":[16],"problems":[18,20,35],"(e.g.,":[19],"expressible":[21],"monadic":[23],"second-order":[24,27],"logic":[25],"with":[26],"quantification":[28],"on":[29],"vertex":[30],"sets,":[31],"which":[32],"includes":[33],"NP-hard":[34],"such":[36],"as":[37],"3-colorability)":[38],"can":[39],"be":[40,60],"solved":[41],"polynomial":[43,64],"time":[44,65],"for":[45],"graphs":[46],"bounded":[48],"clique-width.":[49],"We":[50,70],"show":[51,72],"clique-width":[54,85,106],"given":[57,74],"cannot":[59],"absolutely":[61],"approximated":[62],"unless":[66],"$P":[67],"=":[68],"NP$.":[69],"also":[71],"that,":[73],"G":[77,87],"and":[78],"an":[79],"integer":[80],"k,":[81],"deciding":[82],"whether":[83],"at":[89],"most":[90],"k":[91],"NP-complete.":[93],"This":[94],"solves":[95],"problem":[97],"has":[99],"been":[100],"open":[101],"since":[102],"introduction":[104],"early":[109],"1990s.":[110]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":18},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}