{"id":"https://openalex.org/W2498887162","doi":"https://doi.org/10.1051/ro/2015053","title":"Exploring the disjunctive rank of some facet-inducing inequalities of the acyclic coloring polytope","display_name":"Exploring the disjunctive rank of some facet-inducing inequalities of the acyclic coloring polytope","publication_year":2015,"publication_date":"2015-11-13","ids":{"openalex":"https://openalex.org/W2498887162","doi":"https://doi.org/10.1051/ro/2015053","mag":"2498887162"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2015053","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2015053","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.numdam.org/item/10.1051/ro/2015053.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046545523","display_name":"M\u00f3nica Braga","orcid":"https://orcid.org/0000-0001-8268-8328"},"institutions":[{"id":"https://openalex.org/I35953669","display_name":"National University of General Sarmiento","ror":"https://ror.org/01k6h2m87","country_code":"AR","type":"education","lineage":["https://openalex.org/I35953669"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"M\u00f3nica Braga","raw_affiliation_strings":["Sciences Institute, National University of General Sarmiento J.M. Gutierrez 1150, (B1613 GSX) Los Polvorines, Argentina"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sciences Institute, National University of General Sarmiento J.M. Gutierrez 1150, (B1613 GSX) Los Polvorines, Argentina","institution_ids":["https://openalex.org/I35953669"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019508865","display_name":"Javier Marenco","orcid":"https://orcid.org/0000-0003-2694-4758"},"institutions":[{"id":"https://openalex.org/I35953669","display_name":"National University of General Sarmiento","ror":"https://ror.org/01k6h2m87","country_code":"AR","type":"education","lineage":["https://openalex.org/I35953669"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Javier Marenco","raw_affiliation_strings":["Sciences Institute, National University of General Sarmiento J.M. Gutierrez 1150, (B1613 GSX) Los Polvorines, Argentina"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sciences Institute, National University of General Sarmiento J.M. Gutierrez 1150, (B1613 GSX) Los Polvorines, Argentina","institution_ids":["https://openalex.org/I35953669"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I35953669"],"apc_list":{"value":0,"currency":"EUR","value_usd":0},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.22780269,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"50","issue":"3","first_page":"627","last_page":"644"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.8259412050247192},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.8111615180969238},{"id":"https://openalex.org/keywords/facet","display_name":"Facet (psychology)","score":0.7896832227706909},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6734580993652344},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6464137434959412},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.5238859057426453},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.504170298576355},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4557395577430725},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.41378480195999146},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36506420373916626},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18699002265930176},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12603655457496643},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.09308424592018127},{"id":"https://openalex.org/keywords/social-psychology","display_name":"Social psychology","score":0.08043783903121948},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.06596827507019043},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.050195902585983276}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8259412050247192},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.8111615180969238},{"id":"https://openalex.org/C43122875","wikidata":"https://www.wikidata.org/wiki/Q5428522","display_name":"Facet (psychology)","level":4,"score":0.7896832227706909},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6734580993652344},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6464137434959412},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5238859057426453},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.504170298576355},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4557395577430725},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.41378480195999146},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36506420373916626},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18699002265930176},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12603655457496643},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.09308424592018127},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.08043783903121948},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.06596827507019043},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.050195902585983276},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C187288502","wikidata":"https://www.wikidata.org/wiki/Q641118","display_name":"Personality","level":2,"score":0.0},{"id":"https://openalex.org/C2865642","wikidata":"https://www.wikidata.org/wiki/Q378132","display_name":"Big Five personality traits","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ro/2015053","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2015053","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:RO_2016__50_3_627_0","is_oa":true,"landing_page_url":"http://www.numdam.org/articles/10.1051/ro/2015053/","pdf_url":"https://www.numdam.org/item/10.1051/ro/2015053.pdf","source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:numdam.org:RO_2016__50_3_627_0","is_oa":true,"landing_page_url":"http://www.numdam.org/articles/10.1051/ro/2015053/","pdf_url":"https://www.numdam.org/item/10.1051/ro/2015053.pdf","source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},"sustainable_development_goals":[{"score":0.6100000143051147,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2498887162.pdf","grobid_xml":"https://content.openalex.org/works/W2498887162.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1501678245","https://openalex.org/W1607580485","https://openalex.org/W1963564197","https://openalex.org/W1970193303","https://openalex.org/W1972168259","https://openalex.org/W1988922349","https://openalex.org/W1995561370","https://openalex.org/W2018995959","https://openalex.org/W2024908972","https://openalex.org/W2049143039","https://openalex.org/W2052022404","https://openalex.org/W2058139201","https://openalex.org/W2076535438","https://openalex.org/W2077397558","https://openalex.org/W2087975652","https://openalex.org/W2106264302","https://openalex.org/W2118910553","https://openalex.org/W2124855066","https://openalex.org/W2127906323","https://openalex.org/W2133400152","https://openalex.org/W2143263735","https://openalex.org/W2148872782","https://openalex.org/W2473711771","https://openalex.org/W2963362520","https://openalex.org/W4206058855"],"related_works":["https://openalex.org/W4297449612","https://openalex.org/W3105548266","https://openalex.org/W1976967559","https://openalex.org/W2963459254","https://openalex.org/W2018146720","https://openalex.org/W4310904699","https://openalex.org/W1925942709","https://openalex.org/W2047683846","https://openalex.org/W2044902158","https://openalex.org/W2082154838"],"abstract_inverted_index":{"In":[0,26],"a":[1,54,64],"previous":[2],"work":[3,28],"we":[4,29,58],"presented":[5],"six":[6],"facet-inducing":[7],"families":[8],"of":[9,21,63],"valid":[10,65],"inequalities":[11],"for":[12],"the":[13,22,60],"polytope":[14],"associated":[15],"to":[16,52],"an":[17],"integer":[18],"programming":[19],"formulation":[20],"acyclic":[23],"coloring":[24],"problem.":[25],"this":[27],"study":[30,53],"their":[31],"disjunctive":[32,61],"rank,":[33],"as":[34],"defined":[35],"by":[36],"[E.":[37],"Balas,":[38],"S.":[39],"Ceria":[40],"and":[41],"G.":[42],"Cornu\u00e9jols,":[43],"Math.":[44],"Program.":[45],"58":[46],"(1993)":[47],"295\u2013324].":[48],"We":[49],"also":[50],"propose":[51],"dual":[55],"concept,":[56],"which":[57],"call":[59],"anti-rank":[62],"inequality.":[66]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}