{"id":"https://openalex.org/W1549089996","doi":"https://doi.org/10.37236/373","title":"Symmetric Bowtie Decompositions of the Complete Graph","display_name":"Symmetric Bowtie Decompositions of the Complete Graph","publication_year":2010,"publication_date":"2010-07-20","ids":{"openalex":"https://openalex.org/W1549089996","doi":"https://doi.org/10.37236/373","mag":"1549089996"},"language":"en","primary_location":{"id":"doi:10.37236/373","is_oa":true,"landing_page_url":"https://doi.org/10.37236/373","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r101/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/v17i1r101/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030010535","display_name":"Simona Bonvicini","orcid":"https://orcid.org/0000-0001-5318-7866"},"institutions":[{"id":"https://openalex.org/I122346577","display_name":"University of Modena and Reggio Emilia","ror":"https://ror.org/02d4c4y02","country_code":"IT","type":"education","lineage":["https://openalex.org/I122346577"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Simona Bonvicini","raw_affiliation_strings":["Dipartimento di Scienze e Metodi dell'Ingegneria Via Amendola 2, Pad. Morselli, 42100 Reggio Emilia, Italy","Univ of Modena and Reggio Emilia"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Scienze e Metodi dell'Ingegneria Via Amendola 2, Pad. Morselli, 42100 Reggio Emilia, Italy","institution_ids":[]},{"raw_affiliation_string":"Univ of Modena and Reggio Emilia","institution_ids":["https://openalex.org/I122346577"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015800745","display_name":"Beatrice Ruini","orcid":"https://orcid.org/0000-0001-8007-0751"},"institutions":[{"id":"https://openalex.org/I122346577","display_name":"University of Modena and Reggio Emilia","ror":"https://ror.org/02d4c4y02","country_code":"IT","type":"education","lineage":["https://openalex.org/I122346577"]},{"id":"https://openalex.org/I4210157811","display_name":"Centro di Ricerca in Matematica Pura ed Applicata","ror":"https://ror.org/04fv5g904","country_code":"IT","type":"nonprofit","lineage":["https://openalex.org/I4210157811"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Beatrice Ruini","raw_affiliation_strings":["Dipartimento di Matematica Pura ed Applicata Via Campi 213/b, 41125 Modena, Italy","Univ of Modena and Reggio Emilia"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica Pura ed Applicata Via Campi 213/b, 41125 Modena, Italy","institution_ids":["https://openalex.org/I4210157811"]},{"raw_affiliation_string":"Univ of Modena and Reggio Emilia","institution_ids":["https://openalex.org/I122346577"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030010535"],"corresponding_institution_ids":["https://openalex.org/I122346577"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04542254,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9998999834060669,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9983000159263611,"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/T11130","display_name":"Coding theory and cryptography","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/mathematics","display_name":"Mathematics","score":0.8882585167884827},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8539344072341919},{"id":"https://openalex.org/keywords/dihedral-group","display_name":"Dihedral group","score":0.7901523113250732},{"id":"https://openalex.org/keywords/cyclic-group","display_name":"Cyclic group","score":0.5620436072349548},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5590612888336182},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.4903714656829834},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.47900956869125366},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4667798578739166},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.4667644202709198},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4527074694633484},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.42564675211906433},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.42072999477386475},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.41136303544044495},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.367209792137146},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07296323776245117}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8882585167884827},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8539344072341919},{"id":"https://openalex.org/C72409365","wikidata":"https://www.wikidata.org/wiki/Q558339","display_name":"Dihedral group","level":3,"score":0.7901523113250732},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.5620436072349548},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5590612888336182},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.4903714656829834},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.47900956869125366},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4667798578739166},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.4667644202709198},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4527074694633484},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.42564675211906433},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.42072999477386475},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.41136303544044495},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.367209792137146},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07296323776245117},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/373","is_oa":true,"landing_page_url":"https://doi.org/10.37236/373","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r101/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:iris.unimore.it:11380/644538","is_oa":true,"landing_page_url":"http://hdl.handle.net/11380/644538","pdf_url":"http://hdl.handle.net/11380/644538","source":{"id":"https://openalex.org/S4306400718","display_name":"IRIS UNIMORE (University of Modena and Reggio Emilia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122346577","host_organization_name":"University of Modena and Reggio Emilia","host_organization_lineage":["https://openalex.org/I122346577"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.178.82","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.178.82","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/Volume_17/PDF/v17i1r101.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/373","is_oa":true,"landing_page_url":"https://doi.org/10.37236/373","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r101/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/W1549089996.pdf","grobid_xml":"https://content.openalex.org/works/W1549089996.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W47719751","https://openalex.org/W143975303","https://openalex.org/W1984807967","https://openalex.org/W2018694299","https://openalex.org/W2047578628","https://openalex.org/W2064878508","https://openalex.org/W2073519242","https://openalex.org/W2083005893","https://openalex.org/W2090146723","https://openalex.org/W2153032448","https://openalex.org/W2328212828","https://openalex.org/W2490728539","https://openalex.org/W2798943694","https://openalex.org/W4250917170","https://openalex.org/W6600922036","https://openalex.org/W6601212426","https://openalex.org/W6607606998","https://openalex.org/W6608393273","https://openalex.org/W6608544447","https://openalex.org/W6631124304","https://openalex.org/W6854949419"],"related_works":["https://openalex.org/W2386856003","https://openalex.org/W2738934671","https://openalex.org/W3013930408","https://openalex.org/W4313642480","https://openalex.org/W3005870866","https://openalex.org/W2380219554","https://openalex.org/W2765754501","https://openalex.org/W1970066599","https://openalex.org/W1618945637","https://openalex.org/W2239778148"],"abstract_inverted_index":{"Given":[0],"a":[1,62,148,164,210],"bowtie":[2,150],"decomposition":[3,151],"of":[4,19,29,36,54,69,89,104,134,139,147,163,169,182,187],"the":[5,17,20,27,30,33,37,51,67,80,86,96,132,137,145,161,180,185],"complete":[6],"graph":[7],"$K_v$":[8,140,188],"admitting":[9,109],"an":[10,101,110],"automorphism":[11,111],"group":[12,31,53,63,81,88,97,103,112],"$G$":[13,49,82,98,135,183,196],"acting":[14,64],"transitively":[15,65],"on":[16,66,115,136,184],"vertices":[18,68,116,138,186],"graph,":[21],"we":[22,74],"give":[23],"necessary":[24],"conditions":[25,42],"involving":[26],"rank":[28],"and":[32,71,157],"cycle":[34],"types":[35],"permutations":[38],"in":[39],"$G$.":[40],"These":[41],"yield":[43],"non\u2013existence":[44,76],"results":[45],"for":[46,77,93],"instance":[47],"when":[48,79,95,154,207],"is":[50,83,99,117,128,141,152,158,189,197,209],"dihedral":[52],"order":[55,90,105,170],"$2v$,":[56],"with":[57],"$v\\equiv":[58,155],"1,":[59],"9\\pmod{12}$,":[60],"or":[61,92,121],"$K_9$":[70],"$K_{21}$.":[72],"Furthermore,":[73],"have":[75],"$K_{13}$":[78],"different":[84],"from":[85],"cyclic":[87],"$13$":[91],"$K_{25}$":[94],"not":[100],"abelian":[102],"$25$.":[106],"Bowtie":[107],"decompositions":[108],"whose":[113],"action":[114,133,181],"sharply":[118,142],"transitive,":[119,143],"primitive":[120],"$1$\u2013rotational,":[122],"respectively,":[123],"are":[124,173],"also":[125],"studied.":[126],"It":[127],"shown":[129],"that":[130],"if":[131,179],"then":[144,202],"existence":[146,162,178,203],"$G$\u2013invariant":[149,165],"excluded":[153,206],"9\\pmod{12}$":[156],"equivalent":[159],"to":[160,176,191,199],"Steiner":[166],"triple":[167],"system":[168],"$v$.":[171],"We":[172],"always":[174],"able":[175],"exclude":[177],"assumed":[190,198],"be":[192,205],"$1$\u2013rotational.":[193],"If,":[194],"instead,":[195],"act":[200],"primitively":[201],"can":[204],"$v$":[208],"prime":[211],"power":[212],"satisfying":[213],"some":[214],"additional":[215],"arithmetic":[216],"constraint.":[217]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}