{"id":"https://openalex.org/W3196189097","doi":"https://doi.org/10.3390/sym13081539","title":"Coloring Properties of Mixed Cycloids","display_name":"Coloring Properties of Mixed Cycloids","publication_year":2021,"publication_date":"2021-08-21","ids":{"openalex":"https://openalex.org/W3196189097","doi":"https://doi.org/10.3390/sym13081539","mag":"3196189097"},"language":"en","primary_location":{"id":"doi:10.3390/sym13081539","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13081539","pdf_url":"https://www.mdpi.com/2073-8994/13/8/1539/pdf?version=1629784469","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/2073-8994/13/8/1539/pdf?version=1629784469","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069718437","display_name":"Gy\u00f6rgy D\u00f3sa","orcid":"https://orcid.org/0000-0002-4909-6694"},"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":"Gy\u00f6rgy D\u00f3sa","raw_affiliation_strings":["Department of Mathematics, University of Pannonia, Egyetem Str. 10, 8200 Veszpr\u00e9m, Hungary"],"raw_orcid":"https://orcid.org/0000-0002-4909-6694","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Pannonia, Egyetem Str. 10, 8200 Veszpr\u00e9m, Hungary","institution_ids":["https://openalex.org/I140275651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076288203","display_name":"Nicholas Newman","orcid":"https://orcid.org/0000-0001-7692-0039"},"institutions":[{"id":"https://openalex.org/I149292303","display_name":"Troy University","ror":"https://ror.org/029jj9438","country_code":"US","type":"education","lineage":["https://openalex.org/I149292303"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nicholas Newman","raw_affiliation_strings":["Department of Mathematics and Statistics, Troy University, 600 University Ave., Troy, AL 36082, USA"],"raw_orcid":"https://orcid.org/0000-0001-7692-0039","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Troy University, 600 University Ave., Troy, AL 36082, USA","institution_ids":["https://openalex.org/I149292303"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026437192","display_name":"\u0179solt Tuza","orcid":"https://orcid.org/0000-0003-3235-9221"},"institutions":[{"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"]},{"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":true,"raw_author_name":"Zsolt Tuza","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Re\u00e1ltanoda Str. 13\u201315, 1053 Budapest, Hungary","Department of Computer Science and Systems Technology, University of Pannonia, Egyetem Str. 10, 8200 Veszpr\u00e9m, Hungary"],"raw_orcid":"https://orcid.org/0000-0003-3235-9221","affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Re\u00e1ltanoda Str. 13\u201315, 1053 Budapest, Hungary","institution_ids":["https://openalex.org/I127817813"]},{"raw_affiliation_string":"Department of Computer Science and Systems Technology, University of Pannonia, Egyetem Str. 10, 8200 Veszpr\u00e9m, Hungary","institution_ids":["https://openalex.org/I140275651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051273344","display_name":"Vitaly Voloshin","orcid":"https://orcid.org/0000-0002-9631-5976"},"institutions":[{"id":"https://openalex.org/I149292303","display_name":"Troy University","ror":"https://ror.org/029jj9438","country_code":"US","type":"education","lineage":["https://openalex.org/I149292303"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vitaly Voloshin","raw_affiliation_strings":["Department of Mathematics and Statistics, Troy University, 600 University Ave., Troy, AL 36082, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Troy University, 600 University Ave., Troy, AL 36082, USA","institution_ids":["https://openalex.org/I149292303"]}]}],"institutions":[],"countries_distinct_count":2,"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":0.2033,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.51413621,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"13","issue":"8","first_page":"1539","last_page":"1539"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9929999709129333,"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":0.9929999709129333,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9004999995231628,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.8601381182670593},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.7061375975608826},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.648452877998352},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.5886942148208618},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.507946789264679},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4345053434371948},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.4157696068286896},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.21204602718353271},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17315039038658142}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8601381182670593},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.7061375975608826},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.648452877998352},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.5886942148208618},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.507946789264679},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4345053434371948},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.4157696068286896},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.21204602718353271},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17315039038658142},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13081539","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13081539","pdf_url":"https://www.mdpi.com/2073-8994/13/8/1539/pdf?version=1629784469","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:3e3b6d2f80d44234b8d7d1f4db2a841f","is_oa":true,"landing_page_url":"https://doaj.org/article/3e3b6d2f80d44234b8d7d1f4db2a841f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 8, p 1539 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/8/1539/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13081539","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","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13081539","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13081539","pdf_url":"https://www.mdpi.com/2073-8994/13/8/1539/pdf?version=1629784469","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/G4745933073","display_name":null,"funder_award_id":"SNN 129364","funder_id":"https://openalex.org/F4320336675","funder_display_name":"National Research, Development and Innovation Office"}],"funders":[{"id":"https://openalex.org/F4320336675","display_name":"National Research, Development and Innovation Office","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3196189097.pdf"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W9910222","https://openalex.org/W115381882","https://openalex.org/W189617261","https://openalex.org/W1977037154","https://openalex.org/W1978255035","https://openalex.org/W1979601578","https://openalex.org/W2057823561","https://openalex.org/W2059416008","https://openalex.org/W2066859294","https://openalex.org/W2092863811","https://openalex.org/W2188516493","https://openalex.org/W2731844250","https://openalex.org/W2911383922","https://openalex.org/W3096216201","https://openalex.org/W3155336173","https://openalex.org/W3210639412","https://openalex.org/W4251626892","https://openalex.org/W4285719527","https://openalex.org/W6600396159","https://openalex.org/W6607716295","https://openalex.org/W6740074660","https://openalex.org/W6793205441","https://openalex.org/W6803627486"],"related_works":["https://openalex.org/W4376608589","https://openalex.org/W3135784370","https://openalex.org/W4287273005","https://openalex.org/W2776473626","https://openalex.org/W1966028935","https://openalex.org/W1998397199","https://openalex.org/W2068040398","https://openalex.org/W2949537674","https://openalex.org/W2950770309","https://openalex.org/W2794228661"],"abstract_inverted_index":{"In":[0,13,50],"this":[1],"paper,":[2],"we":[3,126],"investigate":[4],"partitions":[5],"of":[6,21,37,47,94,118,130,137,149,152],"highly":[7],"symmetrical":[8],"discrete":[9],"structures":[10],"called":[11],"cycloids.":[12],"general,":[14],"a":[15,29,53,57,66,75,83,113,150],"mixed":[16,54,58,131],"hypergraph":[17,59],"has":[18,34,44],"two":[19,35,45],"types":[20],"hyperedges.":[22],"The":[23],"vertices":[24,36,46,61,73,81,153],"are":[25],"colored":[26],"in":[27,65,85],"such":[28],"way":[30],"that":[31,96,111],"each":[32,42],"C-edge":[33],"the":[38,86,91,121,128,134,146],"same":[39],"color,":[40],"and":[41,69,77,103,123],"D-edge":[43,84],"distinct":[48],"colors.":[49],"our":[51],"case,":[52],"cycloid":[55],"is":[56,145],"whose":[60],"can":[62,97],"be":[63,98],"arranged":[64],"cyclic":[67],"order,":[68],"every":[70,78],"consecutive":[71,79],"p":[72],"form":[74,82],"C-edge,":[76],"q":[80],"ordering.":[87],"We":[88,106],"completely":[89],"determine":[90],"maximum":[92,135],"number":[93,117,136],"colors":[95,119,138],"used":[99],"for":[100],"any":[101,104,116],"p\u22653":[102],"q\u22652.":[105],"also":[107],"develop":[108],"an":[109],"algorithm":[110],"generates":[112],"coloring":[114],"with":[115,140],"between":[120],"minimum":[122],"maximum.":[124],"Finally,":[125],"discuss":[127],"colorings":[129],"cycloids":[132],"when":[133],"coincides":[139],"its":[141],"upper":[142],"bound,":[143],"which":[144],"largest":[147],"cardinality":[148],"set":[151],"containing":[154],"no":[155],"C-edge.":[156]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}