{"id":"https://openalex.org/W2595005536","doi":"https://doi.org/10.37236/1171","title":"The Smallest One-Realization of a Given Set","display_name":"The Smallest One-Realization of a Given Set","publication_year":2012,"publication_date":"2012-01-16","ids":{"openalex":"https://openalex.org/W2595005536","doi":"https://doi.org/10.37236/1171","mag":"2595005536"},"language":"en","primary_location":{"id":"doi:10.37236/1171","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1171","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p19/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p19/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053402584","display_name":"Ping Zhao","orcid":"https://orcid.org/0000-0003-2639-9841"},"institutions":[{"id":"https://openalex.org/I15823474","display_name":"Linyi University","ror":"https://ror.org/01knv0402","country_code":"CN","type":"education","lineage":["https://openalex.org/I15823474"]},{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ping Zhao","raw_affiliation_strings":["Sch. Math. Sci. & Lab. Math. Com. Sys. Beijing Normal University, Beijing 100875, China","School of Science, Linyi University, Linyi, Shandong, 276005, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sch. Math. Sci. & Lab. Math. Com. Sys. Beijing Normal University, Beijing 100875, China","institution_ids":["https://openalex.org/I25254941"]},{"raw_affiliation_string":"School of Science, Linyi University, Linyi, Shandong, 276005, China","institution_ids":["https://openalex.org/I15823474"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017249105","display_name":"Kefeng Diao","orcid":null},"institutions":[{"id":"https://openalex.org/I15823474","display_name":"Linyi University","ror":"https://ror.org/01knv0402","country_code":"CN","type":"education","lineage":["https://openalex.org/I15823474"]},{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kefeng Diao","raw_affiliation_strings":["Sch. Math. Sci. & Lab. Math. Com. Sys. Beijing Normal University, Beijing 100875, China","School of Science, Linyi University, Linyi, Shandong, 276005, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sch. Math. Sci. & Lab. Math. Com. Sys. Beijing Normal University, Beijing 100875, China","institution_ids":["https://openalex.org/I25254941"]},{"raw_affiliation_string":"School of Science, Linyi University, Linyi, Shandong, 276005, China","institution_ids":["https://openalex.org/I15823474"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031042153","display_name":"Kaishun Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I15823474","display_name":"Linyi University","ror":"https://ror.org/01knv0402","country_code":"CN","type":"education","lineage":["https://openalex.org/I15823474"]},{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kaishun Wang","raw_affiliation_strings":["Sch. Math. Sci. & Lab. Math. Com. Sys. Beijing Normal University, Beijing 100875, China","School of Science, Linyi University, Linyi, Shandong, 276005, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sch. Math. Sci. & Lab. Math. Com. Sys. Beijing Normal University, Beijing 100875, China","institution_ids":["https://openalex.org/I25254941"]},{"raw_affiliation_string":"School of Science, Linyi University, Linyi, Shandong, 276005, China","institution_ids":["https://openalex.org/I15823474"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7643,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.86331122,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"19","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9835000038146973,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9835000038146973,"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/realization","display_name":"Realization (probability)","score":0.945609986782074},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.839492917060852},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7363619208335876},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.6417822241783142},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.6232129335403442},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5891619920730591},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4314620792865753},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09028100967407227}],"concepts":[{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.945609986782074},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.839492917060852},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7363619208335876},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.6417822241783142},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.6232129335403442},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5891619920730591},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4314620792865753},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09028100967407227},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1171","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1171","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p19/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.227.951","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.227.951","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p19/pdf/","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1171","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1171","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p19/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G186742953","display_name":null,"funder_award_id":"NCET-08","funder_id":"https://openalex.org/F4320334924","funder_display_name":"Program for New Century Excellent Talents in University"},{"id":"https://openalex.org/G5991828480","display_name":null,"funder_award_id":"ZR2009AM013","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7410515142","display_name":null,"funder_award_id":"10871027","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7434092059","display_name":null,"funder_award_id":"NCET-08-0052","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334924","display_name":"Program for New Century Excellent Talents in University","ror":"https://ror.org/01mv9t934"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2595005536.pdf","grobid_xml":"https://content.openalex.org/works/W2595005536.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W115381882","https://openalex.org/W118367033","https://openalex.org/W189617261","https://openalex.org/W2023390895","https://openalex.org/W2066859294","https://openalex.org/W2078747814","https://openalex.org/W2137217287","https://openalex.org/W2994522774","https://openalex.org/W6602844401"],"related_works":["https://openalex.org/W4376608589","https://openalex.org/W3138003926","https://openalex.org/W4300037846","https://openalex.org/W3094179932","https://openalex.org/W3005801850","https://openalex.org/W2950595062","https://openalex.org/W1524556636","https://openalex.org/W1988533413","https://openalex.org/W4287332249","https://openalex.org/W3127534791"],"abstract_inverted_index":{"For":[0],"any":[1],"set":[2,20],"$S$":[3,16,30,37,79],"of":[4,15,29,36,41,58,60,63,78,92,94,98],"positive":[5],"integers,":[6],"a":[7,13,27,34,61,76,99,103],"mixed":[8],"hypergraph":[9],"${\\cal":[10,24],"H}$":[11,25],"is":[12,21,26,33,45,69],"realization":[14,35,62],"if":[17,31],"its":[18,42],"feasible":[19],"$S$,":[22],"furthermore,":[23],"one-realization":[28,77,97],"it":[32],"and":[38,118],"each":[39],"entry":[40],"chromatic":[43],"spectrum":[44],"either":[46],"0":[47],"or":[48],"1.":[49],"Jiang":[50,113],"et":[51,114],"al.":[52,115],"showed":[53],"that":[54,73],"the":[55,90,95],"minimum":[56],"number":[57,91],"vertices":[59,93],"$\\{s,t\\}$":[64],"with":[65,80],"$2\\leq":[66],"s\\leq":[67],"t-2$":[68],"$2t-s$.":[70],"Kr\u00e1l":[71,120],"proved":[72],"there":[74],"exists":[75],"at":[81],"most":[82],"$|S|+2\\max{S}-\\min{S}$":[83],"vertices.":[84],"In":[85],"this":[86],"paper,":[87],"we":[88,105],"determine":[89],"smallest":[96],"given":[100],"set.":[101],"As":[102],"result,":[104],"partially":[106],"solve":[107],"an":[108],"open":[109],"problem":[110],"proposed":[111],"by":[112,119],"in":[116,121],"2002":[117],"2004.":[122]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
