{"id":"https://openalex.org/W2170633983","doi":"https://doi.org/10.1016/s0012-365x(98)00319-7","title":"Modular decomposition and transitive orientation","display_name":"Modular decomposition and transitive orientation","publication_year":1999,"publication_date":"1999-04-01","ids":{"openalex":"https://openalex.org/W2170633983","doi":"https://doi.org/10.1016/s0012-365x(98)00319-7","mag":"2170633983"},"language":"en","primary_location":{"id":"doi:10.1016/s0012-365x(98)00319-7","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0012-365x(98)00319-7","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0012365X98003197/pdf","source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.sciencedirect.com/science/article/pii/S0012365X98003197/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014734580","display_name":"Ross M. McConnell","orcid":null},"institutions":[{"id":"https://openalex.org/I921990950","display_name":"University of Colorado Denver","ror":"https://ror.org/02hh7en24","country_code":"US","type":"education","lineage":["https://openalex.org/I921990950"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ross M. McConnell","raw_affiliation_strings":["Department of Computer Science and Engineering, University of Colorado at Denver, P.O. Box 173364, Denver, CO 80217-3364, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, University of Colorado at Denver, P.O. Box 173364, Denver, CO 80217-3364, USA","institution_ids":["https://openalex.org/I921990950"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111822996","display_name":"Jeremy Spinrad","orcid":null},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jeremy P. Spinrad","raw_affiliation_strings":["Department of Computer Science, Vanderbilt University, Nashville, TN 37235, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Vanderbilt University, Nashville, TN 37235, USA","institution_ids":["https://openalex.org/I200719446"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111822996"],"corresponding_institution_ids":["https://openalex.org/I200719446"],"apc_list":{"value":3320,"currency":"USD","value_usd":3320},"apc_paid":{"value":3320,"currency":"USD","value_usd":3320},"fwci":9.5883,"has_fulltext":true,"cited_by_count":436,"citation_normalized_percentile":{"value":0.98534595,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"201","issue":"1-3","first_page":"189","last_page":"241"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9991999864578247,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9991999864578247,"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":0.7907495498657227},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7753118872642517},{"id":"https://openalex.org/keywords/comparability-graph","display_name":"Comparability graph","score":0.6993863582611084},{"id":"https://openalex.org/keywords/modular-decomposition","display_name":"Modular decomposition","score":0.5848603248596191},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5361815094947815},{"id":"https://openalex.org/keywords/clique-graph","display_name":"Clique graph","score":0.5016162395477295},{"id":"https://openalex.org/keywords/transitive-reduction","display_name":"Transitive reduction","score":0.4947752356529236},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.48874711990356445},{"id":"https://openalex.org/keywords/cograph","display_name":"Cograph","score":0.4612376391887665},{"id":"https://openalex.org/keywords/block-graph","display_name":"Block graph","score":0.4568735659122467},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.44229114055633545},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.39856648445129395},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.39625251293182373},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.27146047353744507},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.263963907957077}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7907495498657227},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7753118872642517},{"id":"https://openalex.org/C198414033","wikidata":"https://www.wikidata.org/wiki/Q5155607","display_name":"Comparability graph","level":5,"score":0.6993863582611084},{"id":"https://openalex.org/C187407849","wikidata":"https://www.wikidata.org/wiki/Q6889712","display_name":"Modular decomposition","level":5,"score":0.5848603248596191},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5361815094947815},{"id":"https://openalex.org/C189239283","wikidata":"https://www.wikidata.org/wiki/Q17101022","display_name":"Clique graph","level":5,"score":0.5016162395477295},{"id":"https://openalex.org/C129691609","wikidata":"https://www.wikidata.org/wiki/Q3088151","display_name":"Transitive reduction","level":5,"score":0.4947752356529236},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.48874711990356445},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.4612376391887665},{"id":"https://openalex.org/C43413943","wikidata":"https://www.wikidata.org/wiki/Q4927193","display_name":"Block graph","level":5,"score":0.4568735659122467},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.44229114055633545},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.39856648445129395},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.39625251293182373},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.27146047353744507},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.263963907957077}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1016/s0012-365x(98)00319-7","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0012-365x(98)00319-7","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0012365X98003197/pdf","source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.30.2298","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.2298","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://carbon.cudenver.edu/~rmcconne/linto.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.45.1338","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.1338","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.math.tu-berlin.de/pub/Preprints/combi/Report-475-1995.ps.Z","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.93.6190","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.93.6190","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.colostate.edu/~rmm/linto.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1016/s0012-365x(98)00319-7","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0012-365x(98)00319-7","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0012365X98003197/pdf","source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2170633983.pdf","grobid_xml":"https://content.openalex.org/works/W2170633983.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W20372564","https://openalex.org/W63547832","https://openalex.org/W1512568107","https://openalex.org/W1576293797","https://openalex.org/W1826194655","https://openalex.org/W1964604240","https://openalex.org/W1971322036","https://openalex.org/W1974006935","https://openalex.org/W1985495277","https://openalex.org/W1994038277","https://openalex.org/W2000763343","https://openalex.org/W2003177089","https://openalex.org/W2006512646","https://openalex.org/W2006955534","https://openalex.org/W2008587336","https://openalex.org/W2009049598","https://openalex.org/W2013934077","https://openalex.org/W2014488291","https://openalex.org/W2015906942","https://openalex.org/W2024491681","https://openalex.org/W2027604814","https://openalex.org/W2028503265","https://openalex.org/W2028775537","https://openalex.org/W2033520777","https://openalex.org/W2047899424","https://openalex.org/W2056697294","https://openalex.org/W2068681665","https://openalex.org/W2089692770","https://openalex.org/W2094742636","https://openalex.org/W2111070448","https://openalex.org/W2143474538","https://openalex.org/W2166555321","https://openalex.org/W2169586176","https://openalex.org/W2325654786","https://openalex.org/W2914415208","https://openalex.org/W4299866835","https://openalex.org/W6634597943","https://openalex.org/W6674493442","https://openalex.org/W6684580988"],"related_works":["https://openalex.org/W2764268078","https://openalex.org/W2094742636","https://openalex.org/W4294408013","https://openalex.org/W1692115765","https://openalex.org/W2088435189","https://openalex.org/W1556070262","https://openalex.org/W2761380983","https://openalex.org/W2019334888","https://openalex.org/W4386374895","https://openalex.org/W2170633983"],"abstract_inverted_index":{"A":[0,85],"module":[1],"of":[2,10,23,32,47,68,75,116,120],"an":[3,93],"undirected":[4],"graph":[5,77,86,90],"is":[6,25,34,39,59,65,83,87,95],"a":[7,40,48,70,76,88],"set":[8],"X":[9,24,33],"nodes":[11],"such":[12,92],"for":[13,44,103,128],"each":[14,73],"node":[15],"x":[16],"not":[17],"in":[18],"X,":[19],"either":[20],"every":[21],"member":[22,31],"adjacent":[26,35],"to":[27,36,56,72],"x,":[28],"or":[29],"no":[30],"x.":[37],"There":[38],"canonical":[41],"linear-space":[42],"representation":[43],"the":[45,51,60,66,80,114,121],"modules":[46],"graph,":[49],"called":[50],"modular":[52,57,104],"decomposition.":[53],"Closely":[54],"related":[55],"decomposition":[58,105],"transitive":[61,107],"orientation":[62],"problem,":[63],"which":[64],"problem":[67],"assigning":[69],"direction":[71],"edge":[74],"so":[78],"that":[79],"resulting":[81],"digraph":[82],"transitive.":[84],"comparability":[89,139,146],"if":[91],"assignment":[94],"possible.":[96],"We":[97],"give":[98],"O(n":[99],"+":[100],"m)":[101],"algorithms":[102],"and":[106,111,118,134,141,148],"orientation,":[108],"where":[109],"n":[110],"m":[112],"are":[113],"number":[115],"vertices":[117],"edges":[119],"graph.":[122],"This":[123],"gives":[124],"linear":[125],"time":[126],"bounds":[127],"recognizing":[129],"permutation":[130],"graphs,":[131,140],"maximum":[132],"clique":[133],"minimum":[135],"vertex":[136],"coloring":[137],"on":[138,145],"other":[142],"combinatorial":[143],"problems":[144],"graphs":[147],"their":[149],"complements.":[150]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":18},{"year":2018,"cited_by_count":44},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":18},{"year":2015,"cited_by_count":17},{"year":2014,"cited_by_count":20},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":17}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}