{"id":"https://openalex.org/W4310888018","doi":"https://doi.org/10.1137/21m1423117","title":"Large Rainbow Cliques in Randomly Perturbed Dense Graphs","display_name":"Large Rainbow Cliques in Randomly Perturbed Dense Graphs","publication_year":2022,"publication_date":"2022-12-01","ids":{"openalex":"https://openalex.org/W4310888018","doi":"https://doi.org/10.1137/21m1423117"},"language":"en","primary_location":{"id":"doi:10.1137/21m1423117","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1423117","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029280195","display_name":"Elad Aigner\u2010Horev","orcid":"https://orcid.org/0000-0002-9207-0596"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I52170813","display_name":"Ariel University","ror":"https://ror.org/03nz8qe97","country_code":"IL","type":"education","lineage":["https://openalex.org/I52170813"]}],"countries":["GB","IL"],"is_corresponding":false,"raw_author_name":"Elad Aigner-Horev","raw_affiliation_strings":["\\dagger Department of Computer Science, Ariel University, Ariel 40700, Israel","\\ddagger Department of Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK"],"raw_orcid":"https://orcid.org/0000-0002-9207-0596","affiliations":[{"raw_affiliation_string":"\\dagger Department of Computer Science, Ariel University, Ariel 40700, Israel","institution_ids":["https://openalex.org/I52170813"]},{"raw_affiliation_string":"\\ddagger Department of Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001435782","display_name":"Oran Danon","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I52170813","display_name":"Ariel University","ror":"https://ror.org/03nz8qe97","country_code":"IL","type":"education","lineage":["https://openalex.org/I52170813"]}],"countries":["GB","IL"],"is_corresponding":false,"raw_author_name":"Oran Danon","raw_affiliation_strings":["\\dagger Department of Computer Science, Ariel University, Ariel 40700, Israel","\\ddagger Department of Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\\dagger Department of Computer Science, Ariel University, Ariel 40700, Israel","institution_ids":["https://openalex.org/I52170813"]},{"raw_affiliation_string":"\\ddagger Department of Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072848658","display_name":"Dan Hefetz","orcid":"https://orcid.org/0000-0001-8923-3879"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I52170813","display_name":"Ariel University","ror":"https://ror.org/03nz8qe97","country_code":"IL","type":"education","lineage":["https://openalex.org/I52170813"]}],"countries":["GB","IL"],"is_corresponding":false,"raw_author_name":"Dan Hefetz","raw_affiliation_strings":["\\dagger Department of Computer Science, Ariel University, Ariel 40700, Israel","\\ddagger Department of Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK"],"raw_orcid":"https://orcid.org/0000-0001-8923-3879","affiliations":[{"raw_affiliation_string":"\\dagger Department of Computer Science, Ariel University, Ariel 40700, Israel","institution_ids":["https://openalex.org/I52170813"]},{"raw_affiliation_string":"\\ddagger Department of Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048698980","display_name":"Shoham Letzter","orcid":"https://orcid.org/0000-0003-1193-2017"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I52170813","display_name":"Ariel University","ror":"https://ror.org/03nz8qe97","country_code":"IL","type":"education","lineage":["https://openalex.org/I52170813"]}],"countries":["GB","IL"],"is_corresponding":true,"raw_author_name":"Shoham Letzter","raw_affiliation_strings":["\\dagger Department of Computer Science, Ariel University, Ariel 40700, Israel","\\ddagger Department of Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\\dagger Department of Computer Science, Ariel University, Ariel 40700, Israel","institution_ids":["https://openalex.org/I52170813"]},{"raw_affiliation_string":"\\ddagger Department of Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5048698980"],"corresponding_institution_ids":["https://openalex.org/I241749","https://openalex.org/I52170813"],"apc_list":null,"apc_paid":null,"fwci":1.0889,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.74513338,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"36","issue":"4","first_page":"2975","last_page":"2994"},"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":0.9998999834060669,"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/T11329","display_name":"Limits and Structures in Graph Theory","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/T10374","display_name":"Advanced Graph Theory Research","score":0.9977999925613403,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.8423264026641846},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7463937401771545},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6139013171195984},{"id":"https://openalex.org/keywords/rainbow","display_name":"Rainbow","score":0.507759690284729},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.47936373949050903},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47511348128318787},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37238484621047974},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1516149342060089},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05835610628128052}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8423264026641846},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7463937401771545},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6139013171195984},{"id":"https://openalex.org/C2776558979","wikidata":"https://www.wikidata.org/wiki/Q1052","display_name":"Rainbow","level":2,"score":0.507759690284729},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.47936373949050903},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47511348128318787},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37238484621047974},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1516149342060089},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05835610628128052}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1423117","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1423117","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5384043511","display_name":null,"funder_award_id":"822/18","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W115873615","https://openalex.org/W1490238079","https://openalex.org/W1518503060","https://openalex.org/W1970285613","https://openalex.org/W1971079746","https://openalex.org/W1971734630","https://openalex.org/W1997512277","https://openalex.org/W2006605460","https://openalex.org/W2015373594","https://openalex.org/W2023163209","https://openalex.org/W2033599053","https://openalex.org/W2034838716","https://openalex.org/W2037951482","https://openalex.org/W2058619174","https://openalex.org/W2064298921","https://openalex.org/W2064782937","https://openalex.org/W2067023564","https://openalex.org/W2097225291","https://openalex.org/W2098884097","https://openalex.org/W2127274797","https://openalex.org/W2171469198","https://openalex.org/W2478722229","https://openalex.org/W2615363413","https://openalex.org/W2804858272","https://openalex.org/W2907936830","https://openalex.org/W2950781851","https://openalex.org/W2962757025","https://openalex.org/W2962779128","https://openalex.org/W2963646905","https://openalex.org/W2963959484","https://openalex.org/W2964241396","https://openalex.org/W2964263579","https://openalex.org/W2965629112","https://openalex.org/W2977322974","https://openalex.org/W2977660455","https://openalex.org/W2987824872","https://openalex.org/W3000289468","https://openalex.org/W3008591388","https://openalex.org/W3015052924","https://openalex.org/W3038100514","https://openalex.org/W3093041038","https://openalex.org/W3100678396","https://openalex.org/W3101050805","https://openalex.org/W3101759291","https://openalex.org/W3104767166","https://openalex.org/W3217137612","https://openalex.org/W4243880374","https://openalex.org/W4247942259"],"related_works":["https://openalex.org/W2394414377","https://openalex.org/W2386551956","https://openalex.org/W2374811656","https://openalex.org/W2500362344","https://openalex.org/W2759102619","https://openalex.org/W1480985150","https://openalex.org/W223516324","https://openalex.org/W4300815962","https://openalex.org/W2949690312","https://openalex.org/W128077073"],"abstract_inverted_index":{"For":[0,197],"two":[1],"graphs":[2],"$G$":[3,11,52,222],"and":[4,62,200,226],"$H$,":[5],"write":[6],"$G":[7,48,92,167,216],"\\stackrel{\\mathrm{rbw}}{\\longrightarrow}":[8,95,170,217],"H$":[9,218],"if":[10],"has":[12],"the":[13,30,46,87,90,110,130,144,162,165,183,189,192],"property":[14,91,166],"that":[15,67,105,161,214],"every":[16,98,138,177],"proper":[17],"coloring":[18],"of":[19,26,45,191],"its":[20],"edges":[21,209],"yields":[22],"a":[23,65,83,121],"rainbow":[24],"copy":[25],"$H$.":[27],"We":[28],"study":[29],"thresholds":[31],"for":[32,89,97,106,132,137,152,164,176],"such":[33],"so-called":[34],"anti-Ramsey":[35],"properties":[36],"in":[37,75,82,116,156,181,201],"randomly":[38],"perturbed":[39],"dense":[40],"graphs,":[41],"which":[42],"are":[43,210],"unions":[44],"form":[47],"\\cup":[49,93,168],"\\mathbb{G}(n,p)$,":[50],"where":[51],"is":[53,64,112,120,146,174,223,228],"an":[54],"$n$-vertex":[55],"graph":[56],"with":[57,79],"edge-density":[58],"at":[59,212],"least":[60],"$d$,":[61],"$d$":[63],"constant":[66],"does":[68,185],"not":[69,186],"depend":[70,187],"on":[71,188],"$n$.":[72],"Our":[73],"results":[74,81],"this":[76,101,157],"paper,":[77,85,102,158],"combined":[78],"our":[80,118,149],"companion":[84,150],"determine":[86,160],"threshold":[88,111,131,145,163,184],"\\mathbb{G}(n,p)":[94,169],"K_s$":[96],"$s$.":[99],"In":[100],"we":[103,159],"show":[104],"$s":[107],"\\geq":[108,179],"9$":[109],"$n^{-1/m_2(K_{\\left\\lceil":[113],"s/2":[114],"\\right\\rceil})}$;":[115],"fact,":[117],"$1$-statement":[119],"supersaturation":[122],"result.":[123],"This":[124],"turns":[125],"out":[126],"to":[127],"(almost)":[128],"be":[129],"$s=8$":[133],"as":[134,224],"well,":[135],"but":[136],"$4":[139],"\\leq":[140,142],"s":[141],"7$,":[143],"lower;":[147],"see":[148],"paper":[151],"more":[153],"details.":[154],"Also":[155],"C_{2\\ell":[171],"-":[172,195],"1}$":[173],"$n^{-2}$":[175],"$\\ell":[178],"2$;":[180],"particular,":[182],"length":[190],"cycle":[193],"$C_{2\\ell":[194],"1}$.":[196],"even":[198],"cycles,":[199],"fact":[202],"any":[203],"fixed":[204],"bipartite":[205],"graph,":[206],"no":[207],"random":[208],"needed":[211],"all;":[213],"is,":[215],"always":[219],"holds,":[220],"whenever":[221],"above":[225],"$H$":[227],"bipartite.":[229]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}
