{"id":"https://openalex.org/W2551359169","doi":"https://doi.org/10.1287/moor.2017.0880","title":"Characterizing Polytopes in the 0/1-Cube with Bounded Chv\u00e1tal-Gomory Rank","display_name":"Characterizing Polytopes in the 0/1-Cube with Bounded Chv\u00e1tal-Gomory Rank","publication_year":2018,"publication_date":"2018-01-17","ids":{"openalex":"https://openalex.org/W2551359169","doi":"https://doi.org/10.1287/moor.2017.0880","mag":"2551359169"},"language":"en","primary_location":{"id":"doi:10.1287/moor.2017.0880","is_oa":false,"landing_page_url":"http://doi.org/10.1287/moor.2017.0880","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://dipot.ulb.ac.be/dspace/bitstream/2013/264087/4/benchetrit2018.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069786840","display_name":"Yohann Benchetrit","orcid":null},"institutions":[{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Yohann Benchetrit","raw_affiliation_strings":["Universit\u00e9 Libre de Bruxelles, B-1050 Brussels, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Libre de Bruxelles, B-1050 Brussels, Belgium","institution_ids":["https://openalex.org/I132053463"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001781037","display_name":"Samuel Fiorini","orcid":"https://orcid.org/0000-0002-6845-9008"},"institutions":[{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Samuel Fiorini","raw_affiliation_strings":["Universit\u00e9 Libre de Bruxelles, B-1050 Brussels, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Libre de Bruxelles, B-1050 Brussels, Belgium","institution_ids":["https://openalex.org/I132053463"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007554852","display_name":"Tony Huynh","orcid":"https://orcid.org/0000-0002-6908-923X"},"institutions":[{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Tony Huynh","raw_affiliation_strings":["Universit\u00e9 Libre de Bruxelles, B-1050 Brussels, Belgium"],"raw_orcid":"https://orcid.org/0000-0002-6908-923X","affiliations":[{"raw_affiliation_string":"Universit\u00e9 Libre de Bruxelles, B-1050 Brussels, Belgium","institution_ids":["https://openalex.org/I132053463"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023809656","display_name":"Stefan Weltge","orcid":"https://orcid.org/0000-0002-0102-8326"},"institutions":[{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Stefan Weltge","raw_affiliation_strings":["Universit\u00e9 Libre de Bruxelles, B-1050 Brussels, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Libre de Bruxelles, B-1050 Brussels, Belgium","institution_ids":["https://openalex.org/I132053463"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5069786840"],"corresponding_institution_ids":["https://openalex.org/I132053463"],"apc_list":null,"apc_paid":null,"fwci":0.8549,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.74585532,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"43","issue":"3","first_page":"718","last_page":"725"},"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":0.9998000264167786,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9991000294685364,"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/combinatorics","display_name":"Combinatorics","score":0.8709006309509277},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.8433096408843994},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8238376379013062},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6926387548446655},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.6690141558647156},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6000187397003174},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.49542009830474854},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45621931552886963},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4394400417804718},{"id":"https://openalex.org/keywords/facet","display_name":"Facet (psychology)","score":0.42990776896476746}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8709006309509277},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.8433096408843994},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8238376379013062},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6926387548446655},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.6690141558647156},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6000187397003174},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.49542009830474854},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45621931552886963},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4394400417804718},{"id":"https://openalex.org/C43122875","wikidata":"https://www.wikidata.org/wiki/Q5428522","display_name":"Facet (psychology)","level":4,"score":0.42990776896476746},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"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},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1287/moor.2017.0880","is_oa":false,"landing_page_url":"http://doi.org/10.1287/moor.2017.0880","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:inm:ormoor:v:43:y:2018:i:3:p:718-725","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2017.0880","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:dipot.ulb.ac.be:2013/264087","is_oa":true,"landing_page_url":"https://dipot.ulb.ac.be/dspace/bitstream/2013/264087/4/benchetrit2018.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of operations research, 43 (3","raw_type":"info:ulb-repo/semantics/openurl/article"},{"id":"pmh:oai:iris.uniroma1.it:11573/1707611","is_oa":false,"landing_page_url":"https://hdl.handle.net/11573/1707611","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:dipot.ulb.ac.be:2013/264087","is_oa":true,"landing_page_url":"https://dipot.ulb.ac.be/dspace/bitstream/2013/264087/4/benchetrit2018.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of operations research, 43 (3","raw_type":"info:ulb-repo/semantics/openurl/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W6806899","https://openalex.org/W1487406052","https://openalex.org/W1568620904","https://openalex.org/W1862363755","https://openalex.org/W2011805810","https://openalex.org/W2068848618","https://openalex.org/W2099246938","https://openalex.org/W2145243417","https://openalex.org/W2476232195","https://openalex.org/W2481713999","https://openalex.org/W2567811846","https://openalex.org/W2569749172","https://openalex.org/W2767413753","https://openalex.org/W2950966885","https://openalex.org/W4213311856","https://openalex.org/W4300568640"],"related_works":["https://openalex.org/W1996256832","https://openalex.org/W2099246938","https://openalex.org/W2791467357","https://openalex.org/W1568620904","https://openalex.org/W2147422606","https://openalex.org/W2953085781","https://openalex.org/W2101620967","https://openalex.org/W2066149379","https://openalex.org/W2951043270","https://openalex.org/W2551359169"],"abstract_inverted_index":{"Let":[0,79],"S":[1,35,149],"\u2286":[2],"{0,":[3,19],"1}":[4,20],"n":[5,15,21],"and":[6,39,64,116,169],"R":[7,17,27,131,157],"be":[8],"any":[9],"polytope":[10],"contained":[11,179],"in":[12,94,180],"[0,":[13],"1]":[14],"with":[16,62],"\u2229":[18],"=":[22],"S.":[23,95],"We":[24,96,144],"prove":[25,97,146],"that":[26,34,51,98,127,147,184,212],"has":[28,36,150],"bounded":[29,37,40,133,216],"Chv\u00e1tal-Gomory":[30],"rank":[31],"(CG-rank)":[32],"provided":[33],"notch":[38,44,115,151],"gap,":[41],"where":[42],"the":[43,46,56,65,71,74,84,87,91,114,117,128,138,154,181,213,221],"is":[45,67,132,158,215,227],"minimum":[47],"integer":[48],"p":[49],"such":[50],"all":[52],"p-dimensional":[53],"faces":[54],"of":[55,70,73,77,86,108,130,137,140,156,167,223],"0/1-cube":[57],"have":[58,185],"a":[59,68,106,109,135,164,186,218],"nonempty":[60],"intersection":[61],"S,":[63],"gap":[66,118],"measure":[69],"size":[72],"facet":[75],"coefficients":[76],"conv(S).":[78],"[Formula:":[80,100,141,224],"see":[81,101,142,225],"text]":[82,102,226],"denote":[83],"subgraph":[85],"n-cube":[88],"induced":[89],"by":[90,217],"vertices":[92],"not":[93,104],"if":[99,148,220],"does":[103],"contain":[105],"subdivision":[107],"large":[110],"complete":[111],"graph,":[112],"then":[113,153],"are":[119],"bounded.":[120,160],"By":[121],"our":[122],"main":[123],"result,":[124],"this":[125],"implies":[126],"CG-rank":[129,155,214],"as":[134],"function":[136],"treewidth":[139,222],"text].":[143],"also":[145],"3,":[152],"always":[159],"Both":[161],"results":[162],"generalize":[163],"recent":[165],"theorem":[166],"Cornu\u00e9jols":[168],"Lee":[170,173],"[Cornu\u00e9jols":[171],"G,":[172],"D":[174],"(2016)":[175],"On":[176],"some":[177],"polytopes":[178],"0,1":[182],"hypercube":[183],"small":[187],"Chv\u00e1tal":[188],"rank.":[189],"Louveaux":[190],"Q,":[191],"Skutella":[192],"M,":[193],"eds.":[194],"Proc.":[195],"18th":[196],"Internat.":[197],"Conf.":[198],"Integer":[199],"Programming":[200],"Combinatorial":[201],"Optim.,":[202],"IPCO":[203],"\u201916":[204],"(Springer":[205],"International,":[206],"Cham,":[207],"Switzerland),":[208],"300\u2013311],":[209],"who":[210],"proved":[211],"constant":[219],"at":[228],"most":[229],"2.":[230]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}