{"id":"https://openalex.org/W2519921651","doi":"https://doi.org/10.1137/15m1049361","title":"Transversal Game on Hypergraphs and the $\\frac{3}{4}$-Conjecture on the Total Domination Game","display_name":"Transversal Game on Hypergraphs and the $\\frac{3}{4}$-Conjecture on the Total Domination Game","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2519921651","doi":"https://doi.org/10.1137/15m1049361","mag":"2519921651"},"language":"en","primary_location":{"id":"doi:10.1137/15m1049361","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1049361","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on 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/A5085425895","display_name":"Csilla Bujt\u00e1s","orcid":"https://orcid.org/0000-0002-0511-5291"},"institutions":[{"id":"https://openalex.org/I24027795","display_name":"University of Johannesburg","ror":"https://ror.org/04z6c2n17","country_code":"ZA","type":"education","lineage":["https://openalex.org/I24027795"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"Csilla Bujt\u00e1s","raw_affiliation_strings":["Department of Pure and Applied Mathematics University of Johannesburg Auckland Park, 2006 South Africa"],"affiliations":[{"raw_affiliation_string":"Department of Pure and Applied Mathematics University of Johannesburg Auckland Park, 2006 South Africa","institution_ids":["https://openalex.org/I24027795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089473322","display_name":"Michael A. Henning","orcid":"https://orcid.org/0000-0001-8185-067X"},"institutions":[{"id":"https://openalex.org/I140275651","display_name":"University of Pannonia","ror":"https://ror.org/03y5egs41","country_code":"HU","type":"education","lineage":["https://openalex.org/I140275651"]},{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"funder","lineage":["https://openalex.org/I7597260"]},{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Michael A. Henning","raw_affiliation_strings":["Department of Computer Science and Systems Technology University of Pannonia H-8200 Veszpr\u00e9m, Egyetem u. 10, Hungary","Alfr\u00e9d R\u00e9nyi Institute of Mathematics Hungarian Academy of Sciences H-1053 Budapest, Re\u00e1ltanoda u. 13-15, Hungary"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Systems Technology University of Pannonia H-8200 Veszpr\u00e9m, Egyetem u. 10, Hungary","institution_ids":["https://openalex.org/I140275651"]},{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics Hungarian Academy of Sciences H-1053 Budapest, Re\u00e1ltanoda u. 13-15, Hungary","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026437192","display_name":"\u0179solt Tuza","orcid":"https://orcid.org/0000-0003-3235-9221"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zsolt Tuza","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085425895"],"corresponding_institution_ids":["https://openalex.org/I24027795"],"apc_list":null,"apc_paid":null,"fwci":6.2725,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.96636896,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"30","issue":"3","first_page":"1830","last_page":"1847"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9973999857902527,"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":0.9973999857902527,"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":0.9912999868392944,"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"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9290000200271606,"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/combinatorics","display_name":"Combinatorics","score":0.8858975172042847},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8428552150726318},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.8320727944374084},{"id":"https://openalex.org/keywords/transversal","display_name":"Transversal (combinatorics)","score":0.7911343574523926},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7862511873245239},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.6001172065734863},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5718885064125061},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5158326029777527},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3696058988571167},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.123198002576828},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.05974322557449341}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8858975172042847},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8428552150726318},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.8320727944374084},{"id":"https://openalex.org/C2780130068","wikidata":"https://www.wikidata.org/wiki/Q2208651","display_name":"Transversal (combinatorics)","level":2,"score":0.7911343574523926},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7862511873245239},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.6001172065734863},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5718885064125061},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5158326029777527},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3696058988571167},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.123198002576828},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.05974322557449341},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/15m1049361","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1049361","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:real.mtak.hu:39781","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400081","display_name":"Repository of the Academy's Library (Library of the Hungarian Academy of Sciences)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210140733","host_organization_name":"Library and Information Centre of the Hungarian Academy of Sciences","host_organization_lineage":["https://openalex.org/I4210140733"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W648979152","https://openalex.org/W1494890830","https://openalex.org/W1524397983","https://openalex.org/W1559821680","https://openalex.org/W1598828859","https://openalex.org/W1964163546","https://openalex.org/W1981965088","https://openalex.org/W1987632301","https://openalex.org/W1988939889","https://openalex.org/W1994669980","https://openalex.org/W2051320892","https://openalex.org/W2052275226","https://openalex.org/W2073093064","https://openalex.org/W2073362670","https://openalex.org/W2074131327","https://openalex.org/W2089632810","https://openalex.org/W2096007494","https://openalex.org/W2136564671","https://openalex.org/W2232004157","https://openalex.org/W2315008457","https://openalex.org/W4246941747"],"related_works":["https://openalex.org/W2772332644","https://openalex.org/W1603162376","https://openalex.org/W2914515209","https://openalex.org/W1564907238","https://openalex.org/W2366416021","https://openalex.org/W2153126276","https://openalex.org/W4234443931","https://openalex.org/W1570878271","https://openalex.org/W1486064475","https://openalex.org/W2512442007"],"abstract_inverted_index":{"The":[0],"$\\frac{3}{4}$-Game":[1,156],"Total":[2,157],"Domination":[3,158],"Conjecture":[4,159],"posed":[5],"by":[6,47,58],"Henning,":[7],"Klav\u017ear,":[8],"and":[9,76,89,99,106],"Rall":[10],"[Combinatorica,":[11],"(2016)]":[12],"states":[13],"that":[14,78,129],"if":[15,79,130],"$G$":[16,131],"is":[17,132,160],"a":[18,55,60,73,133,150],"graph":[19,134],"on":[20,135],"$n$":[21,136],"vertices":[22,105,137],"in":[23,63,109,118],"which":[24],"every":[25,80],"component":[26],"contains":[27],"at":[28,86,141,170],"least":[29,87,142,171],"three":[30],"vertices,":[31],"then":[32,93,144],"$\\gamma_{tg}(G)":[33],"\\le":[34,95],"\\frac{3}{4}n$,":[35],"where":[36,97],"$\\gamma_{tg}(G)$":[37],"denotes":[38],"the":[39,52,67,102,114,155,163],"game":[40,62,68],"total":[41],"domination":[42],"number":[43,103],"of":[44,72,82,104,124,152,165],"$G$.":[45],"Motivated":[46],"this":[48,119,125,153],"conjecture,":[49],"we":[50,112,127],"raise":[51],"problem":[53],"to":[54],"higher":[56],"level":[57],"introducing":[59],"transversal":[61,69],"hypergraphs.":[64],"We":[65],"define":[66],"number,":[70],"$\\tau_g(H)$,":[71],"hypergraph":[74],"$H$,":[75],"prove":[77,128],"edge":[81],"$H$":[83],"has":[84],"size":[85],"2,":[88,143],"$H":[90],"\\ncong":[91],"C_4$,":[92],"$\\tau_g(H)":[94],"\\frac{4}{11}(n_{_H}+m_{_H})$,":[96],"$n_{_H}$":[98],"$m_{_H}$":[100],"denote":[101],"edges,":[107],"respectively,":[108],"$H$.":[110],"Further,":[111],"characterize":[113],"hypergraphs":[115],"achieving":[116],"equality":[117],"bound.":[120],"As":[121,149],"an":[122],"application":[123],"result,":[126,154],"with":[138,167],"minimum":[139,168],"degree":[140,169],"$\\gamma_{{tg}}(G)":[145],"<":[146],"\\frac{8}{11}":[147],"n$.":[148],"consequence":[151],"true":[161],"over":[162],"class":[164],"graphs":[166],"2.":[172]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
