{"id":"https://openalex.org/W4417181526","doi":"https://doi.org/10.1002/jgt.23290","title":"On the Minimum Number of Inversions to Make a Digraph k\u2010(Arc\u2010)Strong","display_name":"On the Minimum Number of Inversions to Make a Digraph k\u2010(Arc\u2010)Strong","publication_year":2025,"publication_date":"2025-12-09","ids":{"openalex":"https://openalex.org/W4417181526","doi":"https://doi.org/10.1002/jgt.23290"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.23290","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.23290","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-05470637","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011951093","display_name":"Julien Duron","orcid":null},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Julien Duron","raw_affiliation_strings":["Institute of Informatics University of Warsaw Warsaw Poland","Institute of Informatics, University of Warsaw  Warsaw Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Informatics University of Warsaw Warsaw Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"Institute of Informatics, University of Warsaw  Warsaw Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031575825","display_name":"Fr\u00e9d\u00e9ric Havet","orcid":"https://orcid.org/0000-0002-3447-8112"},"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/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Havet","raw_affiliation_strings":["CNRS, Inria, I3S, Sophia Antipolis Universit\u00e9 C\u00f4te d'Azur Nice France","CNRS, Inria, I3S, Sophia Antipolis Universit\u00e9 C\u00f4te d'Azur  Nice France"],"raw_orcid":"https://orcid.org/0000-0002-3447-8112","affiliations":[{"raw_affiliation_string":"CNRS, Inria, I3S, Sophia Antipolis Universit\u00e9 C\u00f4te d'Azur Nice France","institution_ids":["https://openalex.org/I201841394","https://openalex.org/I1326498283","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS, Inria, I3S, Sophia Antipolis Universit\u00e9 C\u00f4te d'Azur  Nice France","institution_ids":["https://openalex.org/I201841394","https://openalex.org/I1326498283","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083296983","display_name":"Florian H\u00f6rsch","orcid":"https://orcid.org/0000-0002-5410-613X"},"institutions":[{"id":"https://openalex.org/I4210128801","display_name":"Helmholtz Center for Information Security","ror":"https://ror.org/02njgxr09","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I4210128801"]},{"id":"https://openalex.org/I4210153150","display_name":"Klinikum Saarbr\u00fccken","ror":"https://ror.org/04wg18j80","country_code":"DE","type":"healthcare","lineage":["https://openalex.org/I4210153150"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Florian H\u00f6rsch","raw_affiliation_strings":["CISPA Saarbr\u00fccken Saarbr\u00fccken Germany","CISPA Saarbr\u00fccken  Saarbr\u00fccken Germany"],"raw_orcid":"https://orcid.org/0000-0002-5410-613X","affiliations":[{"raw_affiliation_string":"CISPA Saarbr\u00fccken Saarbr\u00fccken Germany","institution_ids":["https://openalex.org/I4210128801","https://openalex.org/I4210153150"]},{"raw_affiliation_string":"CISPA Saarbr\u00fccken  Saarbr\u00fccken Germany","institution_ids":["https://openalex.org/I4210128801","https://openalex.org/I4210153150"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090133829","display_name":"Cl\u00e9ment Rambaud","orcid":null},"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/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]},{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I4210129409","display_name":"Institut de Biologie de l'\u00c9cole Normale Sup\u00e9rieure","ror":"https://ror.org/03mxktp47","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I154526488","https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I4210096427","https://openalex.org/I4210129409"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cl\u00e9ment Rambaud","raw_affiliation_strings":["CNRS, Inria, I3S, Sophia Antipolis Universit\u00e9 C\u00f4te d'Azur Nice France","DIENS, \u00c9cole normale sup\u00e9rieure, CNRS PSL University Paris France","DIENS, \u00c9cole normale sup\u00e9rieure, CNRS PSL University  Paris France","CNRS, Inria, I3S, Sophia Antipolis Universit\u00e9 C\u00f4te d'Azur  Nice France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, Inria, I3S, Sophia Antipolis Universit\u00e9 C\u00f4te d'Azur Nice France","institution_ids":["https://openalex.org/I201841394","https://openalex.org/I1326498283","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"DIENS, \u00c9cole normale sup\u00e9rieure, CNRS PSL University Paris France","institution_ids":["https://openalex.org/I4210129409","https://openalex.org/I2746051580","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"DIENS, \u00c9cole normale sup\u00e9rieure, CNRS PSL University  Paris France","institution_ids":["https://openalex.org/I4210129409","https://openalex.org/I2746051580","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS, Inria, I3S, Sophia Antipolis Universit\u00e9 C\u00f4te d'Azur  Nice France","institution_ids":["https://openalex.org/I201841394","https://openalex.org/I1326498283","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5083296983"],"corresponding_institution_ids":["https://openalex.org/I4210128801","https://openalex.org/I4210153150"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":1.1106,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.85574553,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"111","issue":"2","first_page":"31","last_page":"62"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.6456000208854675,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.6456000208854675,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.09549999982118607,"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":0.07249999791383743,"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/tournament","display_name":"Tournament","score":0.9337999820709229},{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.9241999983787537},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.7190999984741211},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5663999915122986},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4781000018119812},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.43779999017715454},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4142000079154968}],"concepts":[{"id":"https://openalex.org/C136975688","wikidata":"https://www.wikidata.org/wiki/Q1320634","display_name":"Tournament","level":2,"score":0.9337999820709229},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.9241999983787537},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8535000085830688},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.835099995136261},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7190999984741211},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5663999915122986},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5156999826431274},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4781000018119812},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.43779999017715454},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4142000079154968},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.39100000262260437},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.3411000072956085},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.3095000088214874},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.28769999742507935},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.2736999988555908},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.25619998574256897}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/jgt.23290","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.23290","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-05470637v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-05470637","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Graph Theory, 2025, 111 (2), pp.31-62. ⟨10.1002/jgt.23290⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-05470637v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-05470637","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Graph Theory, 2025, 111 (2), pp.31-62. ⟨10.1002/jgt.23290⟩","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1967262927","https://openalex.org/W1983149300","https://openalex.org/W1991825372","https://openalex.org/W1997890669","https://openalex.org/W2008292658","https://openalex.org/W2009267898","https://openalex.org/W2012287357","https://openalex.org/W2035435951","https://openalex.org/W2062725515","https://openalex.org/W2078458440","https://openalex.org/W2082806890","https://openalex.org/W2091858563","https://openalex.org/W2143698439","https://openalex.org/W2144468478","https://openalex.org/W2160033075","https://openalex.org/W2170151066","https://openalex.org/W2313441277","https://openalex.org/W2335132016","https://openalex.org/W2401610261","https://openalex.org/W2808898944","https://openalex.org/W2913028927","https://openalex.org/W2963555739","https://openalex.org/W4210634265","https://openalex.org/W4240899876","https://openalex.org/W4243493907","https://openalex.org/W4300961889","https://openalex.org/W4385336697","https://openalex.org/W4392843456","https://openalex.org/W4408492419"],"related_works":[],"abstract_inverted_index":{"ABSTRACT":[0],"The":[1],"inversion":[2],"of":[3,6,12,16,19,35,109,121,128],"a":[4,9,41,65,81,97,107,126],"set":[5,56],"vertices":[7],"in":[8],"digraph":[10,45],"consists":[11],"reversing":[13],"the":[14,32,60],"direction":[15],"all":[17],"arcs":[18],".":[20,54,57,157],"We":[21,55,58],"study":[22],"(resp.,":[23,43,132,135],")":[24,31],"which":[25],"is":[26,64,87,103,106,125],"(for":[27],"some":[28,119],"positive":[29,76,92,146],"integer":[30,67,77,93,147],"minimum":[33],"number":[34],"inversions":[36],"needed":[37],"to":[38],"transform":[39],"into":[40],"\u2010arc\u2010strong":[42],"\u2010strong)":[44],"or":[46],"if":[47,105,124],"no":[48],"such":[49,142],"transformation":[50],"exists.":[51],"Note":[52],"that":[53,143],"show":[59],"following":[61],"results":[62],"where":[63],"fixed":[66,75,91],"for":[68,70,73,89,118,137,144],":":[69],"every":[71,138,145,149],";":[72,117,123],"any":[74,90],",":[78,94,113,115,139],"deciding":[79,95],"whether":[80,96],"given":[82,98],"oriented":[83,99],"graph":[84,100],"with":[85,101],"satisfies":[86,102],"NP\u2010complete;":[88,104],"tournament":[108,120,127,150],"order":[110,122,129],"at":[111,130,152],"least":[112,131,153],"then":[114,134],"and":[116,148],"),":[133],");":[136],"there":[140],"exists":[141],"on":[151],"vertices,":[154],"we":[155],"have":[156]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-07T08:38:57.713557","created_date":"2025-12-10T00:00:00"}