{"id":"https://openalex.org/W4377137829","doi":"https://doi.org/10.3390/sym15051114","title":"Minimal Non-C-Perfect Hypergraphs with Circular Symmetry","display_name":"Minimal Non-C-Perfect Hypergraphs with Circular Symmetry","publication_year":2023,"publication_date":"2023-05-19","ids":{"openalex":"https://openalex.org/W4377137829","doi":"https://doi.org/10.3390/sym15051114"},"language":"en","primary_location":{"id":"doi:10.3390/sym15051114","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051114","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1114/pdf?version=1684476933","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/5/1114/pdf?version=1684476933","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091983644","display_name":"P\u00e9ter Bence Czaun","orcid":"https://orcid.org/0009-0007-4268-8340"},"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"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"P\u00e9ter Bence Czaun","raw_affiliation_strings":["Faculty of Information Technology, University of Pannonia, Egyetem Street 10, 8200 Veszpr\u00e9m, Hungary"],"affiliations":[{"raw_affiliation_string":"Faculty of Information Technology, University of Pannonia, Egyetem Street 10, 8200 Veszpr\u00e9m, Hungary","institution_ids":["https://openalex.org/I140275651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047342707","display_name":"P\u00e1l Pusztai","orcid":"https://orcid.org/0000-0003-0111-7094"},"institutions":[{"id":"https://openalex.org/I83579964","display_name":"Sz\u00e9chenyi Istv\u00e1n University","ror":"https://ror.org/04091f946","country_code":"HU","type":"education","lineage":["https://openalex.org/I83579964"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"P\u00e1l Pusztai","raw_affiliation_strings":["Department of Mathematics and Computer Science, Sz\u00e9chenyi Istv\u00e1n University, Egyetem Square 1, 9026 Gy\u0151r, Hungary"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Sz\u00e9chenyi Istv\u00e1n University, Egyetem Square 1, 9026 Gy\u0151r, Hungary","institution_ids":["https://openalex.org/I83579964"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091983645","display_name":"Levente Seb\u0151k","orcid":null},"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"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Levente Seb\u0151k","raw_affiliation_strings":["Faculty of Information Technology, University of Pannonia, Egyetem Street 10, 8200 Veszpr\u00e9m, Hungary"],"affiliations":[{"raw_affiliation_string":"Faculty of Information Technology, University of Pannonia, Egyetem Street 10, 8200 Veszpr\u00e9m, Hungary","institution_ids":["https://openalex.org/I140275651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026437192","display_name":"\u0179solt Tuza","orcid":"https://orcid.org/0000-0003-3235-9221"},"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/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":true,"raw_author_name":"Zsolt Tuza","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Re\u00e1ltanoda Street 13\u201315, 1053 Budapest, Hungary","Faculty of Information Technology, University of Pannonia, Egyetem Street 10, 8200 Veszpr\u00e9m, Hungary"],"affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Re\u00e1ltanoda Street 13\u201315, 1053 Budapest, Hungary","institution_ids":["https://openalex.org/I127817813"]},{"raw_affiliation_string":"Faculty of Information Technology, University of Pannonia, Egyetem Street 10, 8200 Veszpr\u00e9m, Hungary","institution_ids":["https://openalex.org/I140275651"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5026437192"],"corresponding_institution_ids":["https://openalex.org/I127817813","https://openalex.org/I140275651"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04153856,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"5","first_page":"1114","last_page":"1114"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9965000152587891,"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":0.9965000152587891,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9865000247955322,"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":0.9847000241279602,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8337382078170776},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6964187622070312},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6216716766357422},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5895843505859375},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.41373735666275024},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3685825765132904}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8337382078170776},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6964187622070312},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6216716766357422},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5895843505859375},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.41373735666275024},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3685825765132904}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15051114","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051114","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1114/pdf?version=1684476933","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5ce36d9036424f8596c2e099a06f6014","is_oa":true,"landing_page_url":"https://doaj.org/article/5ce36d9036424f8596c2e099a06f6014","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 5, p 1114 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/5/1114/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15051114","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry; Volume 15; Issue 5; Pages: 1114","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15051114","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051114","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1114/pdf?version=1684476933","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1748000517","display_name":null,"funder_award_id":"NKFIH","funder_id":"https://openalex.org/F4320336675","funder_display_name":"National Research, Development and Innovation Office"},{"id":"https://openalex.org/G291844724","display_name":null,"funder_award_id":"SNN 129364","funder_id":"https://openalex.org/F4320322193","funder_display_name":"Nemzeti Kutat\u00e1si \u00e9s Technol\u00f3giai Hivatal"},{"id":"https://openalex.org/G4041839036","display_name":null,"funder_award_id":"SNN 129364","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G4745933073","display_name":null,"funder_award_id":"SNN 129364","funder_id":"https://openalex.org/F4320336675","funder_display_name":"National Research, Development and Innovation Office"},{"id":"https://openalex.org/G6679577976","display_name":null,"funder_award_id":"MILAB","funder_id":"https://openalex.org/F4320336675","funder_display_name":"National Research, Development and Innovation Office"},{"id":"https://openalex.org/G7946896065","display_name":null,"funder_award_id":"129364","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"}],"funders":[{"id":"https://openalex.org/F4320322193","display_name":"Nemzeti Kutat\u00e1si \u00e9s Technol\u00f3giai Hivatal","ror":"https://ror.org/03g2am276"},{"id":"https://openalex.org/F4320326762","display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","ror":null},{"id":"https://openalex.org/F4320336675","display_name":"National Research, Development and Innovation Office","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4377137829.pdf","grobid_xml":"https://content.openalex.org/works/W4377137829.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W130959402","https://openalex.org/W189617261","https://openalex.org/W1856998012","https://openalex.org/W1973199140","https://openalex.org/W2059416008","https://openalex.org/W2188516493","https://openalex.org/W3133863338","https://openalex.org/W3196189097","https://openalex.org/W3210639412","https://openalex.org/W4251626892","https://openalex.org/W6607716295","https://openalex.org/W6740074660","https://openalex.org/W6793205441","https://openalex.org/W6803627486"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4300899577","https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W4393325717","https://openalex.org/W1973978937","https://openalex.org/W121594594","https://openalex.org/W2784911598","https://openalex.org/W3111310291"],"abstract_inverted_index":{"In":[0],"this":[1,90],"research":[2],"paper,":[3],"we":[4],"study":[5],"3-uniform":[6],"hypergraphs":[7,158],"H=(X,E)":[8],"with":[9,110,147],"circular":[10],"symmetry.":[11],"Two":[12],"parameters":[13],"are":[14,103],"considered:":[15],"the":[16,30,50,64,95,111,126],"largest":[17],"size":[18],"\u03b1(H)":[19],"of":[20,34,40,49,73,97,113,117,133,159],"a":[21,37,87,114,152],"set":[22],"S\u2282X":[23],"not":[24],"containing":[25],"any":[26],"edge":[27],"E\u2208E,":[28],"and":[29,125,142,149],"maximum":[31],"number":[32],"\u03c7\u00af(H)":[33],"colors":[35],"in":[36,62],"vertex":[38],"coloring":[39],"H":[41,61,102],"such":[42,101],"that":[43],"each":[44],"E\u2208E":[45],"contains":[46],"two":[47,134],"vertices":[48],"same":[51],"color.":[52],"The":[53],"problem":[54],"considered":[55],"here":[56],"is":[57,80,92,155],"to":[58,89,93,107,122],"characterize":[59],"those":[60],"which":[63],"equality":[65],"\u03c7\u00af(H\u2032)=\u03b1(H\u2032)":[66,79],"holds":[67],"for":[68,157],"every":[69],"induced":[70,136],"subhypergraph":[71],"H\u2032=(X\u2032,E\u2032)":[72],"H.":[74],"A":[75],"well-known":[76],"objection":[77],"against":[78],"where":[81],"\u2229E\u2208E\u2032E=1,":[82],"termed":[83],"\u201cmonostar\u201d.":[84],"Steps":[85],"toward":[86],"solution":[88],"approach":[91],"investigate":[94],"properties":[96],"monostar-free":[98],"structures.":[99],"All":[100],"completely":[104],"identified":[105],"up":[106],"16":[108],"vertices,":[109,144],"aid":[112],"computer.":[115],"Most":[116],"them":[118],"can":[119],"be":[120],"shown":[121],"satisfy":[123],"\u03c7\u00af(H)=\u03b1(H),":[124],"few":[127],"exceptions":[128],"contain":[129],"one":[130],"or":[131],"both":[132,146],"specific":[135],"subhypergraphs":[137],"H5\u2941,":[138],"H6\u2941":[139],"on":[140],"five":[141],"six":[143],"respectively,":[145],"\u03c7\u00af=2":[148],"\u03b1=3.":[150],"Furthermore,":[151],"general":[153],"conjecture":[154],"raised":[156],"prime":[160],"orders.":[161]},"counts_by_year":[],"updated_date":"2026-03-16T09:10:04.655348","created_date":"2025-10-10T00:00:00"}