{"id":"https://openalex.org/W4395959992","doi":"https://doi.org/10.1007/s00493-024-00102-6","title":"Rainbow Variations on a Theme by Mantel: Extremal Problems for Gallai Colouring Templates","display_name":"Rainbow Variations on a Theme by Mantel: Extremal Problems for Gallai Colouring Templates","publication_year":2024,"publication_date":"2024-04-29","ids":{"openalex":"https://openalex.org/W4395959992","doi":"https://doi.org/10.1007/s00493-024-00102-6"},"language":"lv","primary_location":{"id":"doi:10.1007/s00493-024-00102-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-024-00102-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-024-00102-6.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00493-024-00102-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074450972","display_name":"Victor Falgas\u2010Ravry","orcid":"https://orcid.org/0000-0001-8631-4745"},"institutions":[{"id":"https://openalex.org/I90267481","display_name":"Ume\u00e5 University","ror":"https://ror.org/05kb8h459","country_code":"SE","type":"education","lineage":["https://openalex.org/I90267481"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Victor Falgas-Ravry","raw_affiliation_strings":["Institutionen f\u00f6r Matematik och Matematisk Statistik, Ume\u00e5 Universitet, Ume\u00e5, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institutionen f\u00f6r Matematik och Matematisk Statistik, Ume\u00e5 Universitet, Ume\u00e5, Sweden","institution_ids":["https://openalex.org/I90267481"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035765654","display_name":"Klas Markstr\u00f6m","orcid":"https://orcid.org/0000-0002-6344-1642"},"institutions":[{"id":"https://openalex.org/I90267481","display_name":"Ume\u00e5 University","ror":"https://ror.org/05kb8h459","country_code":"SE","type":"education","lineage":["https://openalex.org/I90267481"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Klas Markstr\u00f6m","raw_affiliation_strings":["Institutionen f\u00f6r Matematik och Matematisk Statistik, Ume\u00e5 Universitet, Ume\u00e5, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institutionen f\u00f6r Matematik och Matematisk Statistik, Ume\u00e5 Universitet, Ume\u00e5, Sweden","institution_ids":["https://openalex.org/I90267481"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046680485","display_name":"Eero R\u00e4ty","orcid":null},"institutions":[{"id":"https://openalex.org/I90267481","display_name":"Ume\u00e5 University","ror":"https://ror.org/05kb8h459","country_code":"SE","type":"education","lineage":["https://openalex.org/I90267481"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Eero R\u00e4ty","raw_affiliation_strings":["Institutionen f\u00f6r Matematik och Matematisk Statistik, Ume\u00e5 Universitet, Ume\u00e5, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institutionen f\u00f6r Matematik och Matematisk Statistik, Ume\u00e5 Universitet, Ume\u00e5, Sweden","institution_ids":["https://openalex.org/I90267481"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5035765654"],"corresponding_institution_ids":["https://openalex.org/I90267481"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":{"value":3190,"currency":"USD","value_usd":3190},"fwci":4.2842,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.94358407,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"44","issue":"5","first_page":"977","last_page":"1010"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998000264167786,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998000264167786,"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/T10849","display_name":"Finite Group Theory Research","score":0.9955999851226807,"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":0.9947999715805054,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47420695424079895},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2349967360496521}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47420695424079895},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2349967360496521}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00493-024-00102-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-024-00102-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-024-00102-6.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:DiVA.org:umu-224095","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-224095","pdf_url":"https://umu.diva-portal.org/smash/get/diva2:1858208/FULLTEXT02","source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I86987016","host_organization_name":"KTH Royal Institute of Technology","host_organization_lineage":["https://openalex.org/I86987016"],"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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00493-024-00102-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-024-00102-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-024-00102-6.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4395959992.pdf","grobid_xml":"https://content.openalex.org/works/W4395959992.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W4552026","https://openalex.org/W52585686","https://openalex.org/W1509611772","https://openalex.org/W1591340849","https://openalex.org/W1964543450","https://openalex.org/W1986746825","https://openalex.org/W2000763343","https://openalex.org/W2007516388","https://openalex.org/W2117407892","https://openalex.org/W2168685161","https://openalex.org/W2599261204","https://openalex.org/W2914189553","https://openalex.org/W2962951681","https://openalex.org/W2963611066","https://openalex.org/W2994143791","https://openalex.org/W3007681597","https://openalex.org/W4380877001"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2062023542"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"$$\\textbf{G}:=(G_1,":[2],"G_2,":[3],"G_3)$$":[4],"G":[5,9,12,15,37,62,89,150,169],":":[6],"=":[7],"(":[8,46,128,149],"1":[10,48,73,130],",":[11,14,49,52,74,77,131,134],"2":[13,51,76,133,158],"3":[16,54,79,136],")":[17,55,137,152],"be":[18],"a":[19,39,82,101,172,177,200],"triple":[20,40],"of":[21,29,41,105,119,203],"graphs":[22],"on":[23,193],"the":[24,111,117],"same":[25],"vertex":[26],"set":[27,118],"V":[28],"size":[30],"n.":[31],"A":[32],"rainbow":[33,92,173],"triangle":[34,83],"in":[35,84,107],"$$\\textbf{G}$$":[36,88,168],"is":[38,164],"edges":[42],"$$(e_1,":[43],"e_2,":[44,69],"e_3)$$":[45],"e":[47,50,53,59,72,75,78],"with":[56],"$$e_i\\in":[57],"G_i$$":[58],"i":[60,63,66,151,156,161],"\u2208":[61],"for":[64,159],"each":[65,160],"and":[67,162,187,198,211],"$$\\{e_1,":[68],"e_3\\}$$":[70],"{":[71],"}":[80],"forming":[81],"V.":[85],"The":[86],"triples":[87],"not":[90],"containing":[91],"triangles,":[93],"also":[94],"known":[95],"as":[96],"Gallai":[97,195],"colouring":[98,196],"templates,":[99,197],"are":[100],"widely":[102],"studied":[103],"class":[104],"objects":[106],"extremal":[108,194],"combinatorics.":[109],"In":[110],"present":[112],"work,":[113],"we":[114],"fully":[115],"determine":[116],"edge":[120],"densities":[121],"$$(\\alpha":[122],"_1,":[123],"\\alpha":[124,126,144],"_2,":[125],"_3)$$":[127],"\u03b1":[129,132,135,155],"such":[138],"that":[139],"if":[140],"$$\\vert":[141],"E(G_i)\\vert":[142],">":[143,154],"_i":[145],"n^2$$":[146],"|":[147,153],"E":[148],"n":[157,163],"sufficiently":[165],"large,":[166],"then":[167],"must":[170],"contain":[171],"triangle.":[174],"This":[175],"resolves":[176],"problem":[178],"raised":[179],"by":[180],"Aharoni,":[181],"DeVos,":[182],"de":[183],"la":[184],"Maza,":[185],"Montejanos":[186],"\u0160\u00e1mal,":[188],"generalises":[189],"several":[190],"previous":[191],"results":[192],"proves":[199],"recent":[201],"conjecture":[202],"Frankl,":[204],"Gy\u0151ri,":[205],"He,":[206],"Lv,":[207],"Salia,":[208],"Tompkins,":[209],"Varga":[210],"Zhu.":[212]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}