{"id":"https://openalex.org/W2907936830","doi":"https://doi.org/10.1017/s0963548320000231","title":"Ramsey properties of randomly perturbed graphs: cliques and cycles","display_name":"Ramsey properties of randomly perturbed graphs: cliques and cycles","publication_year":2020,"publication_date":"2020-06-30","ids":{"openalex":"https://openalex.org/W2907936830","doi":"https://doi.org/10.1017/s0963548320000231","mag":"2907936830"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548320000231","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548320000231","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C368E54DCC99B5C0651FE8403BB05FEF/S0963548320000231a.pdf/div-class-title-ramsey-properties-of-randomly-perturbed-graphs-cliques-and-cycles-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C368E54DCC99B5C0651FE8403BB05FEF/S0963548320000231a.pdf/div-class-title-ramsey-properties-of-randomly-perturbed-graphs-cliques-and-cycles-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066263695","display_name":"Shagnik Das","orcid":"https://orcid.org/0009-0004-4487-7741"},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Shagnik Das","raw_affiliation_strings":["Institute of Mathematics, Freie Universit\u00e4t Berlin, Arnimallee 3, 14195 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Freie Universit\u00e4t Berlin, Arnimallee 3, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086607043","display_name":"Andrew Treglown","orcid":"https://orcid.org/0000-0002-4293-5678"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Andrew Treglown","raw_affiliation_strings":["School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK","institution_ids":["https://openalex.org/I79619799"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086607043"],"corresponding_institution_ids":["https://openalex.org/I79619799"],"apc_list":null,"apc_paid":null,"fwci":8.8088,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.99034869,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"29","issue":"6","first_page":"830","last_page":"867"},"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":0.9995999932289124,"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":0.9995999932289124,"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":0.9954000115394592,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9580000042915344,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8206050992012024},{"id":"https://openalex.org/keywords/ramseys-theorem","display_name":"Ramsey's theorem","score":0.71302330493927},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6721706986427307},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.6276634931564331},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6109998822212219},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.487344354391098},{"id":"https://openalex.org/keywords/random-regular-graph","display_name":"Random regular graph","score":0.4260321855545044},{"id":"https://openalex.org/keywords/ramsey-theory","display_name":"Ramsey theory","score":0.4152790606021881},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.24266135692596436},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.23654377460479736}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8206050992012024},{"id":"https://openalex.org/C44115641","wikidata":"https://www.wikidata.org/wiki/Q918099","display_name":"Ramsey's theorem","level":3,"score":0.71302330493927},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6721706986427307},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.6276634931564331},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6109998822212219},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.487344354391098},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.4260321855545044},{"id":"https://openalex.org/C112291201","wikidata":"https://www.wikidata.org/wiki/Q1336170","display_name":"Ramsey theory","level":2,"score":0.4152790606021881},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.24266135692596436},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.23654377460479736}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s0963548320000231","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548320000231","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C368E54DCC99B5C0651FE8403BB05FEF/S0963548320000231a.pdf/div-class-title-ramsey-properties-of-randomly-perturbed-graphs-cliques-and-cycles-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1901.01684","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.01684","pdf_url":"https://arxiv.org/pdf/1901.01684","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/4ff4936d-b358-4b45-a15a-dd8716c44a30","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/4ff4936d-b358-4b45-a15a-dd8716c44a30","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"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":"Das, S & Treglown, A 2020, 'Ramsey properties of randomly perturbed graphs : cliques and cycles', Combinatorics, Probability and Computing, vol. 29, no. 6, pp. 830-867. https://doi.org/10.1017/S0963548320000231","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/4ff4936d-b358-4b45-a15a-dd8716c44a30","is_oa":false,"landing_page_url":"https://www.cambridge.org/core/journals/combinatorics-probability-and-computing","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.1017/s0963548320000231","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548320000231","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C368E54DCC99B5C0651FE8403BB05FEF/S0963548320000231a.pdf/div-class-title-ramsey-properties-of-randomly-perturbed-graphs-cliques-and-cycles-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3916157125","display_name":null,"funder_award_id":"EP/M016641/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2907936830.pdf","grobid_xml":"https://content.openalex.org/works/W2907936830.grobid-xml"},"referenced_works_count":56,"referenced_works":["https://openalex.org/W788200807","https://openalex.org/W1490238079","https://openalex.org/W1551595104","https://openalex.org/W1970285613","https://openalex.org/W1971734630","https://openalex.org/W1992843513","https://openalex.org/W2006605460","https://openalex.org/W2022675369","https://openalex.org/W2029013046","https://openalex.org/W2034622005","https://openalex.org/W2034838716","https://openalex.org/W2037951482","https://openalex.org/W2047452808","https://openalex.org/W2058619174","https://openalex.org/W2064782937","https://openalex.org/W2067023564","https://openalex.org/W2068871408","https://openalex.org/W2099986052","https://openalex.org/W2111007781","https://openalex.org/W2116537669","https://openalex.org/W2122502862","https://openalex.org/W2171469198","https://openalex.org/W2478722229","https://openalex.org/W2761466726","https://openalex.org/W2784877557","https://openalex.org/W2804858272","https://openalex.org/W2885077188","https://openalex.org/W2901710416","https://openalex.org/W2911850936","https://openalex.org/W2962757025","https://openalex.org/W2962779128","https://openalex.org/W2962856385","https://openalex.org/W2963646905","https://openalex.org/W2963733791","https://openalex.org/W2963959484","https://openalex.org/W2964207251","https://openalex.org/W2964241396","https://openalex.org/W2965629112","https://openalex.org/W2981247787","https://openalex.org/W2987824872","https://openalex.org/W3000289468","https://openalex.org/W3015052924","https://openalex.org/W3038100514","https://openalex.org/W3100678396","https://openalex.org/W3101759291","https://openalex.org/W3104767166","https://openalex.org/W3144881883","https://openalex.org/W4235659163","https://openalex.org/W4236551144","https://openalex.org/W4236734508","https://openalex.org/W4242056544","https://openalex.org/W4245585741","https://openalex.org/W4247942259","https://openalex.org/W4248180758","https://openalex.org/W4289281890","https://openalex.org/W4289693762"],"related_works":["https://openalex.org/W2474561564","https://openalex.org/W2949231378","https://openalex.org/W4297961547","https://openalex.org/W2950410478","https://openalex.org/W4301765976","https://openalex.org/W4301914467","https://openalex.org/W4297817664","https://openalex.org/W2292548913","https://openalex.org/W1901246819","https://openalex.org/W2945124636"],"abstract_inverted_index":{"Abstract":[0],"Given":[1],"graphs":[2,63,105,162],"H":[3,6,14,17,40,47,187,193,293,299],"1":[4,15,41,188,294],",":[5,8,16,141,168,200,237,253,272,353],"2":[7,18,48,194,300],"a":[9,36,43,67,83,89,126,180,261,281,338,373],"graph":[10,69,85,128,133,340,345],"G":[11,29],"is":[12,35,66,134,229,346],"(":[13,138,165,234,250,269,350],")":[19,144,240,256,275,356],"-Ramsey":[20,145,241,257,276,357],"if,":[21],"for":[22,247],"every":[23],"colouring":[24],"of":[25,28,39,46,60,92,99,102,155,161,263,319,375,394],"the":[26,58,131,153,184,216,224,233,248,268,285,289,309,320,343,378,381],"edges":[27,94,121,213,333],"with":[30,82,135,260,347],"red":[31,37],"and":[32,75,86,111,192,298,323,363,390],"blue,":[33],"there":[34],"copy":[38,45],"or":[42],"blue":[44],".":[49,64],"In":[50],"this":[51,157,177,227,266],"paper":[52],"we":[53,205,244,307,328,371],"investigate":[54],"Ramsey":[55,100,398],"questions":[56],"in":[57,78,114,183,215,226,288],"setting":[59],"randomly":[61,103],"perturbed":[62,104],"This":[65],"random":[68,93,120,218,332,388,397],"model":[70],"introduced":[71],"by":[72,108],"Bohman,":[73],"Frieze":[74],"Martin":[76],"[8]":[77],"which":[79],"one":[80,209],"starts":[81],"dense":[84,127,339],"then":[87],"adds":[88],"given":[90],"number":[91],"to":[95,125,129,159,232,284,337,341],"it.":[96],"The":[97],"study":[98],"properties":[101],"was":[106],"initiated":[107],"Krivelevich,":[109,321],"Sudakov":[110,322],"Tetali":[112,324],"[30]":[113,325],"2006;":[115],"they":[116],"determined":[117],"how":[118,330],"many":[119,331],"must":[122,334],"be":[123,335],"added":[124,336],"ensure":[130,342],"resulting":[132,344],"high":[136,348],"probability":[137,349],"K":[139,142,166,169,190,196,235,238,251,254,270,273,354],"3":[140,167,236],"t":[143,147,170,197,201,239,255,303,355,364],"(for":[146,358],"\u227d":[148,202,361,365],"3).":[149],"They":[150],"also":[151,279],"raised":[152],"question":[154,287],"generalizing":[156],"result":[158,221,315],"pairs":[160],"other":[163],"than":[164,214],").":[171],"We":[172,278],"make":[173],"significant":[174],"progress":[175],"on":[176],"question,":[178],"giving":[179],"precise":[181,282],"solution":[182,283],"case":[185,228,290],"when":[186,291],"=":[189,195,295,301],"s":[191,199,297,352,360],"where":[198],"5.":[203],"Although":[204],"again":[206],"show":[207],"that":[208,223],"requires":[210],"polynomially":[211],"fewer":[212],"purely":[217],"graph,":[219],"our":[220,369],"shows":[222],"problem":[225],"quite":[230],"different":[231],"question.":[242],"Moreover,":[243],"give":[245,280],"bounds":[246],"corresponding":[249,310],"4":[252,271,274],"question;":[258],"together":[259],"construction":[262],"Powierski":[264],"[37]":[265],"resolves":[267],"problem.":[277,312],"analogous":[286],"both":[292],"C":[296,302,351],"are":[304],"cycles.":[305],"Additionally":[306],"consider":[308],"multicolour":[311],"Our":[313],"final":[314],"gives":[316],"another":[317],"generalization":[318],"result.":[326],"Specifically,":[327],"determine":[329],"odd":[359],"5":[362],"4).":[366],"To":[367],"prove":[368],"results":[370],"combine":[372],"mixture":[374],"approaches,":[376],"employing":[377],"container":[379],"method,":[380],"regularity":[382],"method":[383],"as":[384,386],"well":[385],"dependent":[387],"choice,":[389],"apply":[391],"robust":[392],"extensions":[393],"recent":[395],"asymmetric":[396],"results.":[399]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2020-11-23T00:00:00"}