{"id":"https://openalex.org/W2415629108","doi":"https://doi.org/10.37236/6026","title":"Domination of the Rectangular Queen's Graph","display_name":"Domination of the Rectangular Queen's Graph","publication_year":2019,"publication_date":"2019-12-04","ids":{"openalex":"https://openalex.org/W2415629108","doi":"https://doi.org/10.37236/6026","mag":"2415629108"},"language":"en","primary_location":{"id":"doi:10.37236/6026","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6026","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i4p45/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i4p45/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042358724","display_name":"S\u00e1ndor Boz\u00f3ki","orcid":"https://orcid.org/0000-0003-4170-4613"},"institutions":[{"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"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"S\u00e1ndor Boz\u00f3ki","raw_affiliation_strings":["Hungarian Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Hungarian Academy of Sciences","institution_ids":["https://openalex.org/I7597260"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068316228","display_name":"P\u00e9ter G\u00e1l","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P\u00e9ter G\u00e1l","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019174790","display_name":"Istv\u00e1n Marosi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Istv\u00e1n Marosi","raw_affiliation_strings":["Kofax-Recognita Zrt., Budapest, Hungary"],"affiliations":[{"raw_affiliation_string":"Kofax-Recognita Zrt., Budapest, Hungary","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031500684","display_name":"William D. Weakley","orcid":null},"institutions":[{"id":"https://openalex.org/I4210130184","display_name":"Purdue University Fort Wayne","ror":"https://ror.org/04c4hz115","country_code":"US","type":"education","lineage":["https://openalex.org/I4210130184"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"William D. Weakley","raw_affiliation_strings":["Purdue University Fort Wayne, USA"],"affiliations":[{"raw_affiliation_string":"Purdue University Fort Wayne, USA","institution_ids":["https://openalex.org/I4210130184"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5042358724"],"corresponding_institution_ids":["https://openalex.org/I7597260"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00265859,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"4","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":0.9998000264167786,"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":0.9998000264167786,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9934999942779541,"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"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.8716144561767578},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6968545913696289},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4864177703857422},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4794577360153198},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.45615047216415405},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.4345923066139221},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1664094626903534},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.09762358665466309}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8716144561767578},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6968545913696289},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4864177703857422},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4794577360153198},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.45615047216415405},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.4345923066139221},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1664094626903534},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.09762358665466309}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.37236/6026","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6026","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i4p45/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:unipub.lib.uni-corvinus.hu:7306","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400280","display_name":"Corvinus Research Archive (Corvinus University of Budapest)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I163245316","host_organization_name":"Corvinus University of Budapest","host_organization_lineage":["https://openalex.org/I163245316"],"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"},{"id":"pmh:oai:arXiv.org:1606.02060","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1606.02060","pdf_url":"https://arxiv.org/pdf/1606.02060","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2415629108","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1606.02060.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:eprints.sztaki.hu:9861","is_oa":false,"landing_page_url":"http://eprints.sztaki.hu/9861/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401907","display_name":"SZTAKI Publication Repository (Hungarian Academy of Sciences)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I7597260","host_organization_name":"Hungarian Academy of Sciences","host_organization_lineage":["https://openalex.org/I7597260"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.48550/arxiv.1606.02060","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1606.02060","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.37236/6026","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6026","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i4p45/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/G2061337280","display_name":null,"funder_award_id":"BO/00154/16","funder_id":"https://openalex.org/F4320322192","funder_display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia"},{"id":"https://openalex.org/G2675870313","display_name":null,"funder_award_id":"\u00daNKP-18-4","funder_id":"https://openalex.org/F4320322192","funder_display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia"},{"id":"https://openalex.org/G4936238807","display_name":null,"funder_award_id":"K111797","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"},{"id":"https://openalex.org/G5145119004","display_name":null,"funder_award_id":"\u00daNKP-18-4","funder_id":"https://openalex.org/F4320323476","funder_display_name":"Emberi Eroforr\u00e1sok Miniszt\u00e9riuma"},{"id":"https://openalex.org/G7541558665","display_name":null,"funder_award_id":"Bolyai","funder_id":"https://openalex.org/F4320322192","funder_display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia"},{"id":"https://openalex.org/G8284597927","display_name":null,"funder_award_id":"J\u00e1nos Bolyai","funder_id":"https://openalex.org/F4320322192","funder_display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia"},{"id":"https://openalex.org/G8623428395","display_name":null,"funder_award_id":"111797","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"},{"id":"https://openalex.org/G8959004","display_name":null,"funder_award_id":"J\u00e1nos","funder_id":"https://openalex.org/F4320322192","funder_display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia"}],"funders":[{"id":"https://openalex.org/F4320321994","display_name":"Hungarian Scientific Research Fund","ror":"https://ror.org/00v349e63"},{"id":"https://openalex.org/F4320322192","display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia","ror":"https://ror.org/02ks8qq67"},{"id":"https://openalex.org/F4320323476","display_name":"Emberi Eroforr\u00e1sok Miniszt\u00e9riuma","ror":"https://ror.org/00rb16m44"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2415629108.pdf","grobid_xml":"https://content.openalex.org/works/W2415629108.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W17350985","https://openalex.org/W1487888965","https://openalex.org/W1499418355","https://openalex.org/W1511873780","https://openalex.org/W1884457451","https://openalex.org/W1964459245","https://openalex.org/W2001655229","https://openalex.org/W2014767907","https://openalex.org/W2019635364","https://openalex.org/W2072177531","https://openalex.org/W2072808306","https://openalex.org/W2110753888","https://openalex.org/W2188337130","https://openalex.org/W2752613978","https://openalex.org/W2762915491","https://openalex.org/W2898316331","https://openalex.org/W2988320476","https://openalex.org/W3038027991","https://openalex.org/W6815673699","https://openalex.org/W7005485941"],"related_works":["https://openalex.org/W2999204739","https://openalex.org/W2065461754","https://openalex.org/W2089817321","https://openalex.org/W2766781494","https://openalex.org/W1972652019","https://openalex.org/W2979119835","https://openalex.org/W2770835395","https://openalex.org/W65264223","https://openalex.org/W109072738","https://openalex.org/W1590248699","https://openalex.org/W3082126129","https://openalex.org/W2951821892","https://openalex.org/W3084403602","https://openalex.org/W1968308625","https://openalex.org/W3024996095","https://openalex.org/W3102706553","https://openalex.org/W2797561846","https://openalex.org/W2107079802","https://openalex.org/W2057090129","https://openalex.org/W2953009631"],"abstract_inverted_index":{"The":[0,70,417],"queens":[1,166,186],"graph":[2],"$Q_{m":[3,41,49,56,78,426],"\\times":[4,12,42,50,57,79,88,93,145,149,153,172,180,297,309,342,355,371,427,437,442,482,486,490,494],"n}$":[5,43,51,58,80,428],"has":[6],"the":[7,10,26,33,82,160,170,178,192,200,395,430],"squares":[8,19,39,406,414],"of":[9,32,38,40,55,73,77,91,112,118,320,340,353,405,412,420,425,440],"$m":[11,221,243,253,269,289,304,377],"n$":[13,306],"chessboard":[14],"as":[15],"its":[16,413],"vertices;":[17],"two":[18,185,411],"are":[20,24,103,299,329,349,415,453],"adjacent":[21,64],"if":[22,52,252,268,303,409],"they":[23],"in":[25,61,68,106,123,187,285,344,456],"same":[27],"row,":[28],"column,":[29],"or":[30,63],"diagonal":[31],"board.":[34],"A":[35,403],"set":[36,47,76,404,424],"$D$":[37,62],"is":[44,59,81,202,206,209,280,333,407,429],"a":[45,66,74,110,188],"dominating":[46,75,114,321,423,462],"for":[48,130,242,288,384,467],"every":[53],"square":[54,67,205],"either":[60],"to":[65,121,168,176,335,366],"$D$.":[69],"minimum":[71,113,418,461],"size":[72,419],"domination":[83,198,432],"number,":[84,433],"denoted":[85,434],"by":[86,435],"$\\gamma(Q_{m":[87,92,296,308,341,354,370],"n})$.":[89,438],"Values":[90,439],"n}),":[94,443],"\\,":[95,444],"4":[96,229,445],"\\leq":[97,99,101,196,244,265,277,290,305,378,446,448,450],"m":[98,246,447],"n":[100,379,449],"18,\\,$":[102],"given":[104,398,454],"here,":[105,455],"each":[107,331,457],"case":[108,458],"with":[109,183,233,376,459],"file":[111],"sets":[115,322],"(often":[116],"all":[117],"them,":[119],"up":[120],"symmetry)":[122],"an":[124,234,421],"online":[125,235],"appendix.":[126],"In":[127,301,464],"these":[128,286,465],"ranges":[129,466],"$m$":[131,165,468],"and":[132,267,325,390,393,469,492],"$n$,":[133,470],"monotonicity":[134,352,471],"fails":[135,472],"once:":[136],"$\\gamma(Q_{8\\times":[137],"11})":[138,146,150,475,483,487],"=":[139,143,147,151,215,363,373,387,476,480,484,488,496,500],"6":[140,477],">":[141,478,498],"5":[142,479],"\\gamma(Q_{9":[144],"\\gamma(Q_{10":[148],"\\gamma(Q_{11":[152],"11})$.":[154],"Let":[155],"$g(m)$":[156],"[respectively":[157],"$g^{*}(m)$]":[158],"be":[159,401],"largest":[161],"integer":[162],"such":[163],"that":[164,213,238,282],"suffice":[167],"dominate":[169,177],"$(m+1)":[171,179],"g(m)$":[173],"board":[174,182,201],"[respectively,":[175],"g^{*}(m)$":[181],"no":[184,410],"row].":[189],"Starting":[190],"from":[191,204,360],"elementary":[193],"bound":[194,397],"$g(m)":[195,214],"3m$,":[197],"when":[199,220],"far":[203],"investigated.":[207],"It":[208,279],"shown":[210,281,334],"(Theorem":[211,250],"2)":[212],"3m$":[216],"can":[217,400],"only":[218],"occur":[219,241],"\\equiv":[222,254,270],"0,":[223],"1,":[224],"2,":[225],"3,":[226],"\\mbox{or":[227,257],"}":[228,258],"\\mbox{":[230,260,272],"(mod":[231,261,273],"9)}$,":[232],"appendix":[236],"showing":[237],"this":[239],"does":[240],"40,":[245],"\\neq":[247],"3$.":[248],"Also":[249],"4),":[251],"5,":[255],"6,":[256],"7":[259],"9)}$":[262,274],"then":[263,275,307],"$g^{*}(m)":[264,276],"3m-2$,":[266],"8":[271,499],"3m-4$.":[278],"equality":[283],"holds":[284,357],"bounds":[287,294,339],"40":[291],"$.":[292],"Lower":[293],"on":[295],"n})$":[298,343,356],"given.":[300],"particular,":[302],"n})":[310,372],"\\geq":[311],"\\min":[312],"\\{":[313],"m,\\lceil":[314],"(m+n-2)/4":[315],"\\rceil":[316],"\\}$.":[317],"Two":[318],"types":[319],"(orthodox":[323],"covers":[324],"centrally":[326],"strong":[327],"sets)":[328],"developed;":[330],"type":[332],"give":[336],"good":[337],"upper":[338],"several":[345],"cases.":[346],"Three":[347],"questions":[348],"posed:":[350],"whether":[351,369,394],"(other":[358,382],"than":[359,383],"$(m,":[361,385],"n)":[362,386],"(8,":[364],"11)$":[365],"$(9,":[367],"11)$),":[368,392],"(m+n-2)/4$":[374],"occurs":[375],"<":[380],"3m+2$":[381],"(3,":[388],"3)$":[389],"$(11,":[391],"lower":[396],"above":[399],"improved.":[402],"independent":[408,422,431],"adjacent.":[416],"$i(Q_{m":[436,441],"18,":[451],"\\,$":[452],"some":[460],"sets.":[463],"twice:":[473],"$i(Q_{8\\times":[474],"i(Q_{9":[481],"i(Q_{10":[485],"i(Q_{11":[489],"11})$,":[491],"$i(Q_{11":[493],"18})":[495],"9":[497],"i(Q_{12\\times":[501],"18})$.":[502]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}