{"id":"https://openalex.org/W2145243417","doi":"https://doi.org/10.1016/0012-365x(73)90167-2","title":"Edmonds polytopes and a hierarchy of combinatorial problems","display_name":"Edmonds polytopes and a hierarchy of combinatorial problems","publication_year":1973,"publication_date":"1973-04-01","ids":{"openalex":"https://openalex.org/W2145243417","doi":"https://doi.org/10.1016/0012-365x(73)90167-2","mag":"2145243417"},"language":"en","primary_location":{"id":"doi:10.1016/0012-365x(73)90167-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(73)90167-2","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111486123","display_name":"Va\u0161ek Chv\u00e1tal","orcid":null},"institutions":[{"id":"https://openalex.org/I70931966","display_name":"Universit\u00e9 de Montr\u00e9al","ror":"https://ror.org/0161xgx34","country_code":"CA","type":"education","lineage":["https://openalex.org/I70931966"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"V. Chv\u00e1tal","raw_affiliation_strings":["Centre de Recherches Math\u00e9matiques, Universit\u00e9 de Montr\u00e9al, Canada","Centre de Recherches Math\u00e9matiques, Universit\u00e9 de Montr\u00e9al Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre de Recherches Math\u00e9matiques, Universit\u00e9 de Montr\u00e9al, Canada","institution_ids":["https://openalex.org/I70931966"]},{"raw_affiliation_string":"Centre de Recherches Math\u00e9matiques, Universit\u00e9 de Montr\u00e9al Canada","institution_ids":["https://openalex.org/I70931966"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111486123"],"corresponding_institution_ids":["https://openalex.org/I70931966"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":4.3981,"has_fulltext":false,"cited_by_count":618,"citation_normalized_percentile":{"value":0.95716719,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"4","issue":"4","first_page":"305","last_page":"337"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.994700014591217,"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":0.994700014591217,"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/T11476","display_name":"Graph theory and applications","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9886999726295471,"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/mathematics","display_name":"Mathematics","score":0.8967664837837219},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7836318016052246},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6600876450538635},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.614508330821991},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.6119074821472168},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5721597671508789},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5522286891937256},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5234807729721069},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4926815629005432},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.47385933995246887},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.4585989713668823},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4524364471435547},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4408963918685913},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.42847907543182373},{"id":"https://openalex.org/keywords/linear-inequality","display_name":"Linear inequality","score":0.4147886633872986},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.39362651109695435},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.09712439775466919}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8967664837837219},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7836318016052246},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6600876450538635},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.614508330821991},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.6119074821472168},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5721597671508789},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5522286891937256},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5234807729721069},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4926815629005432},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.47385933995246887},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.4585989713668823},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4524364471435547},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4408963918685913},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.42847907543182373},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.4147886633872986},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.39362651109695435},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.09712439775466919},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/0012-365x(73)90167-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(73)90167-2","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.178.365","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.178.365","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://opim.wharton.upenn.edu/%7Eguignard/916_2007/papers_to_read/chvatal_reprinted_2006.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W86044744","https://openalex.org/W1482143660","https://openalex.org/W1551635709","https://openalex.org/W1972577005","https://openalex.org/W1985061810","https://openalex.org/W1997998268","https://openalex.org/W2009683816","https://openalex.org/W2012959686","https://openalex.org/W2036265926","https://openalex.org/W2045472305","https://openalex.org/W2058408846","https://openalex.org/W2066356146","https://openalex.org/W2072789827","https://openalex.org/W2072848654","https://openalex.org/W2076086747","https://openalex.org/W2078358924","https://openalex.org/W2087310451","https://openalex.org/W2157529519","https://openalex.org/W2177834369","https://openalex.org/W2327315803","https://openalex.org/W2328726307","https://openalex.org/W2401610261","https://openalex.org/W2500722895","https://openalex.org/W2536967169","https://openalex.org/W2795674018","https://openalex.org/W3034528871","https://openalex.org/W4233756358","https://openalex.org/W4249611931","https://openalex.org/W6603474794","https://openalex.org/W6638708274","https://openalex.org/W6644040475","https://openalex.org/W6659573362","https://openalex.org/W6682093759","https://openalex.org/W6724041430"],"related_works":["https://openalex.org/W2228244008","https://openalex.org/W2065436195","https://openalex.org/W4285278887","https://openalex.org/W2995925505","https://openalex.org/W2365237642","https://openalex.org/W3116484972","https://openalex.org/W2941986668","https://openalex.org/W4232431455","https://openalex.org/W12876310","https://openalex.org/W2038958829"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":20},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":40},{"year":2018,"cited_by_count":21},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":23},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":22},{"year":2013,"cited_by_count":25},{"year":2012,"cited_by_count":23}],"updated_date":"2026-05-12T08:28:47.272897","created_date":"2025-10-10T00:00:00"}