{"id":"https://openalex.org/W1495909191","doi":"https://doi.org/10.37236/653","title":"A Recurrence for Bounds on Dominating Sets in $k$-Majority Tournaments","display_name":"A Recurrence for Bounds on Dominating Sets in $k$-Majority Tournaments","publication_year":2011,"publication_date":"2011-08-19","ids":{"openalex":"https://openalex.org/W1495909191","doi":"https://doi.org/10.37236/653","mag":"1495909191"},"language":"en","primary_location":{"id":"doi:10.37236/653","is_oa":true,"landing_page_url":"https://doi.org/10.37236/653","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p166/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/v18i1p166/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055872933","display_name":"Dror Fidler","orcid":"https://orcid.org/0000-0002-8848-0509"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dror Fidler","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055872933"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.04134471,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"18","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9487000107765198,"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":0.9487000107765198,"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/T10991","display_name":"Game Theory and Voting Systems","score":0.9355000257492065,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9045000076293945,"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/tournament","display_name":"Tournament","score":0.915594220161438},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8874094486236572},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8225396871566772},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6992630362510681},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.5325713753700256},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49217692017555237},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4494263827800751},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3464650511741638},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.21743160486221313},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06222143769264221}],"concepts":[{"id":"https://openalex.org/C136975688","wikidata":"https://www.wikidata.org/wiki/Q1320634","display_name":"Tournament","level":2,"score":0.915594220161438},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8874094486236572},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8225396871566772},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6992630362510681},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.5325713753700256},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49217692017555237},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4494263827800751},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3464650511741638},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.21743160486221313},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06222143769264221},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/653","is_oa":true,"landing_page_url":"https://doi.org/10.37236/653","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p166/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"}],"best_oa_location":{"id":"doi:10.37236/653","is_oa":true,"landing_page_url":"https://doi.org/10.37236/653","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p166/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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1495909191.pdf","grobid_xml":"https://content.openalex.org/works/W1495909191.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2148712149","https://openalex.org/W2328184904"],"related_works":["https://openalex.org/W2354251330","https://openalex.org/W2383468429","https://openalex.org/W1981770164","https://openalex.org/W2353691047","https://openalex.org/W2397412345","https://openalex.org/W2910480389","https://openalex.org/W2988746064","https://openalex.org/W2009004645","https://openalex.org/W2886475100","https://openalex.org/W2045621845"],"abstract_inverted_index":{"A":[0],"$k$-majority":[1,65,97],"tournament":[2],"is":[3,53],"realized":[4],"by":[5,60,69,118],"$2k-1$":[6],"linear":[7],"orders":[8],"on":[9],"the":[10,29,41,45,89],"set":[11,95],"of":[12,28,33,43,47,91],"vertices,":[13],"where":[14],"a":[15,48,92],"vertex":[16],"$u$":[17,21],"dominates":[18],"$v$":[19,23],"if":[20],"precedes":[22],"in":[24,96],"at":[25,119],"least":[26],"$k$":[27],"orders.":[30],"Various":[31],"properties":[32],"such":[34],"tournaments":[35,57,66,98,115],"have":[36],"been":[37],"studied,":[38],"among":[39],"them":[40],"problem":[42],"finding":[44],"size":[46,90],"smallest":[49,93],"dominating":[50,94],"set.":[51],"It":[52],"known":[54,79],"that":[55,64,99,113],"$2$-majority":[56],"are":[58,67,77,116],"dominated":[59,68,117],"$3$":[61],"vertices":[62],"and":[63],"$O(k":[70],"\\log":[71],"k)$":[72],"vertices.":[73,122],"However,":[74],"precise":[75],"values":[76],"not":[78],"even":[80],"for":[81,88,105],"$k=3$.":[82],"We":[83],"establish":[84],"new":[85],"upper":[86],"bounds":[87,104],"considerably":[100],"improve":[101],"upon":[102],"previous":[103],"small":[106],"$k$.":[107],"In":[108],"particular":[109],"our":[110],"result":[111],"shows":[112],"$3$-majority":[114],"most":[120],"$12$":[121]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}