{"id":"https://openalex.org/W2078832298","doi":"https://doi.org/10.1007/s13173-011-0047-1","title":"The interval count of interval graphs and orders: a short survey","display_name":"The interval count of interval graphs and orders: a short survey","publication_year":2011,"publication_date":"2011-11-25","ids":{"openalex":"https://openalex.org/W2078832298","doi":"https://doi.org/10.1007/s13173-011-0047-1","mag":"2078832298"},"language":"en","primary_location":{"id":"doi:10.1007/s13173-011-0047-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s13173-011-0047-1","pdf_url":"https://journal-bcs.springeropen.com/counter/pdf/10.1007/s13173-011-0047-1","source":{"id":"https://openalex.org/S69801987","display_name":"Journal of the Brazilian Computer Society","issn_l":"0104-6500","issn":["0104-6500","1678-4804"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Brazilian Computer Society","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://journal-bcs.springeropen.com/counter/pdf/10.1007/s13173-011-0047-1","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035781389","display_name":"M\u00e1rcia R. Cerioli","orcid":"https://orcid.org/0000-0002-9712-3140"},"institutions":[{"id":"https://openalex.org/I122140584","display_name":"Universidade Federal do Rio de Janeiro","ror":"https://ror.org/03490as77","country_code":"BR","type":"education","lineage":["https://openalex.org/I122140584"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"M\u00e1rcia R. Cerioli","raw_affiliation_strings":["COPPE, Universidade Federal do Rio de Janeiro (UFRJ), Caixa Postal 68511, 21941-972, Rio de Janeiro, RJ, Brazil","Instituto de Matem\u00e1tica, Universidade Federal do Rio de Janeiro (UFRJ), Caixa Postal 68530, 21941-972, Rio de Janeiro, RJ, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"COPPE, Universidade Federal do Rio de Janeiro (UFRJ), Caixa Postal 68511, 21941-972, Rio de Janeiro, RJ, Brazil","institution_ids":["https://openalex.org/I122140584"]},{"raw_affiliation_string":"Instituto de Matem\u00e1tica, Universidade Federal do Rio de Janeiro (UFRJ), Caixa Postal 68530, 21941-972, Rio de Janeiro, RJ, Brazil","institution_ids":["https://openalex.org/I122140584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064325807","display_name":"Fabiano S. Oliveira","orcid":"https://orcid.org/0000-0002-8498-2472"},"institutions":[{"id":"https://openalex.org/I122140584","display_name":"Universidade Federal do Rio de Janeiro","ror":"https://ror.org/03490as77","country_code":"BR","type":"education","lineage":["https://openalex.org/I122140584"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Fabiano de S.\u00a0Oliveira","raw_affiliation_strings":["COPPE, Universidade Federal do Rio de Janeiro (UFRJ), Caixa Postal 68511, 21941-972, Rio de Janeiro, RJ, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"COPPE, Universidade Federal do Rio de Janeiro (UFRJ), Caixa Postal 68511, 21941-972, Rio de Janeiro, RJ, Brazil","institution_ids":["https://openalex.org/I122140584"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004984970","display_name":"Jayme L. Szwarcfiter","orcid":"https://orcid.org/0000-0002-7538-7305"},"institutions":[{"id":"https://openalex.org/I122140584","display_name":"Universidade Federal do Rio de Janeiro","ror":"https://ror.org/03490as77","country_code":"BR","type":"education","lineage":["https://openalex.org/I122140584"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Jayme L. Szwarcfiter","raw_affiliation_strings":["COPPE, Universidade Federal do Rio de Janeiro (UFRJ), Caixa Postal 68511, 21941-972, Rio de Janeiro, RJ, Brazil","Instituto de Matem\u00e1tica, Universidade Federal do Rio de Janeiro (UFRJ), Caixa Postal 68530, 21941-972, Rio de Janeiro, RJ, Brazil","N\u00facleo de Computa\u00e7\u00e3o Eletr\u00f4nica, Universidade Federal do Rio de Janeiro (UFRJ), Caixa Postal: 2324, 20010-974, Rio de Janeiro, RJ, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"COPPE, Universidade Federal do Rio de Janeiro (UFRJ), Caixa Postal 68511, 21941-972, Rio de Janeiro, RJ, Brazil","institution_ids":["https://openalex.org/I122140584"]},{"raw_affiliation_string":"Instituto de Matem\u00e1tica, Universidade Federal do Rio de Janeiro (UFRJ), Caixa Postal 68530, 21941-972, Rio de Janeiro, RJ, Brazil","institution_ids":["https://openalex.org/I122140584"]},{"raw_affiliation_string":"N\u00facleo de Computa\u00e7\u00e3o Eletr\u00f4nica, Universidade Federal do Rio de Janeiro (UFRJ), Caixa Postal: 2324, 20010-974, Rio de Janeiro, RJ, Brazil","institution_ids":["https://openalex.org/I122140584"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035781389"],"corresponding_institution_ids":["https://openalex.org/I122140584"],"apc_list":null,"apc_paid":null,"fwci":0.6522,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.70798696,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"18","issue":"2","first_page":"103","last_page":"112"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9628999829292297,"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":0.9628999829292297,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9624000191688538,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11567","display_name":"semigroups and automata theory","score":0.9621000289916992,"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/interval","display_name":"Interval (graph theory)","score":0.8490457534790039},{"id":"https://openalex.org/keywords/interval-graph","display_name":"Interval graph","score":0.7741758227348328},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5509558916091919},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5136823058128357},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4401073455810547},{"id":"https://openalex.org/keywords/interval-data","display_name":"Interval data","score":0.43125060200691223},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3779948353767395},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2957325875759125},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.1858389675617218},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.093189537525177}],"concepts":[{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.8490457534790039},{"id":"https://openalex.org/C67810366","wikidata":"https://www.wikidata.org/wiki/Q835942","display_name":"Interval graph","level":5,"score":0.7741758227348328},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5509558916091919},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5136823058128357},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4401073455810547},{"id":"https://openalex.org/C2983220686","wikidata":"https://www.wikidata.org/wiki/Q951437","display_name":"Interval data","level":3,"score":0.43125060200691223},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3779948353767395},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2957325875759125},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.1858389675617218},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.093189537525177},{"id":"https://openalex.org/C22088475","wikidata":"https://www.wikidata.org/wiki/Q647974","display_name":"Data envelopment analysis","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s13173-011-0047-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s13173-011-0047-1","pdf_url":"https://journal-bcs.springeropen.com/counter/pdf/10.1007/s13173-011-0047-1","source":{"id":"https://openalex.org/S69801987","display_name":"Journal of the Brazilian Computer Society","issn_l":"0104-6500","issn":["0104-6500","1678-4804"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Brazilian Computer Society","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s13173-011-0047-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s13173-011-0047-1","pdf_url":"https://journal-bcs.springeropen.com/counter/pdf/10.1007/s13173-011-0047-1","source":{"id":"https://openalex.org/S69801987","display_name":"Journal of the Brazilian Computer Society","issn_l":"0104-6500","issn":["0104-6500","1678-4804"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Brazilian Computer Society","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320322749","display_name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro","ror":"https://ror.org/03kk0s825"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2078832298.pdf","grobid_xml":"https://content.openalex.org/works/W2078832298.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W65985817","https://openalex.org/W587622775","https://openalex.org/W1480255812","https://openalex.org/W1524764420","https://openalex.org/W1561939243","https://openalex.org/W1854915859","https://openalex.org/W1964154211","https://openalex.org/W1969070807","https://openalex.org/W1969279846","https://openalex.org/W1973007407","https://openalex.org/W1975936206","https://openalex.org/W1984528974","https://openalex.org/W1990242495","https://openalex.org/W1994372089","https://openalex.org/W2004819421","https://openalex.org/W2019128474","https://openalex.org/W2032212328","https://openalex.org/W2037583329","https://openalex.org/W2052186517","https://openalex.org/W2055650273","https://openalex.org/W2060983467","https://openalex.org/W2063909168","https://openalex.org/W2093843227","https://openalex.org/W2106754157","https://openalex.org/W2117560761","https://openalex.org/W2143474538","https://openalex.org/W2166395672","https://openalex.org/W2486958962","https://openalex.org/W2610475167","https://openalex.org/W2611093227","https://openalex.org/W3021221708","https://openalex.org/W3197565569","https://openalex.org/W4232896595","https://openalex.org/W4285719527","https://openalex.org/W4319782100"],"related_works":["https://openalex.org/W115577841","https://openalex.org/W2032833645","https://openalex.org/W4256681807","https://openalex.org/W2078832298","https://openalex.org/W2338920004","https://openalex.org/W2232227265","https://openalex.org/W2045103335","https://openalex.org/W4232843823","https://openalex.org/W2205126926","https://openalex.org/W3139960064"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"interval":[2,10,18,23,26,35,38,47,62],"count":[3,48,63],"problem":[4,49],"determines":[5],"the":[6,29,46,61,70],"smallest":[7],"number":[8,31,71],"of":[9,20,32,72],"lengths":[11],"needed":[12],"in":[13],"order":[14],"to":[15],"represent":[16],"an":[17],"model":[19],"a":[21,42,57,67],"given":[22],"graph":[24,68],"or":[25],"order.":[27],"Despite":[28],"large":[30],"studies":[33],"about":[34,60],"graphs":[36],"and":[37,64,69],"orders,":[39],"surprisingly":[40],"only":[41],"few":[43],"results":[44],"on":[45],"are":[50],"known.":[51],"In":[52],"this":[53],"work,":[54],"we":[55],"provide":[56],"short":[58],"survey":[59],"related":[65],"problems.":[66],"its":[73],"maximal":[74],"cliques.":[75]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}