{"id":"https://openalex.org/W4403304347","doi":"https://doi.org/10.1017/s0963548324000269","title":"A note on extremal constructions for the Erd\u0151s\u2013Rademacher problem","display_name":"A note on extremal constructions for the Erd\u0151s\u2013Rademacher problem","publication_year":2024,"publication_date":"2024-10-10","ids":{"openalex":"https://openalex.org/W4403304347","doi":"https://doi.org/10.1017/s0963548324000269"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548324000269","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548324000269","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/861F9C17713FD1055F58598E6A4F058E/S0963548324000269a.pdf/div-class-title-a-note-on-extremal-constructions-for-the-erd-s-rademacher-problem-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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/861F9C17713FD1055F58598E6A4F058E/S0963548324000269a.pdf/div-class-title-a-note-on-extremal-constructions-for-the-erd-s-rademacher-problem-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075876413","display_name":"Xizhi Liu","orcid":"https://orcid.org/0000-0002-0731-8084"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Xizhi Liu","raw_affiliation_strings":["Mathematics Institute and DIMAP, University of Warwick, Coventry, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Institute and DIMAP, University of Warwick, Coventry, UK","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080095759","display_name":"Oleg Pikhurko","orcid":"https://orcid.org/0000-0002-9657-4011"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Oleg Pikhurko","raw_affiliation_strings":["Mathematics Institute and DIMAP, University of Warwick, Coventry, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Institute and DIMAP, University of Warwick, Coventry, UK","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080095759"],"corresponding_institution_ids":["https://openalex.org/I39555362"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.30992313,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"1","first_page":"52","last_page":"62"},"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":0.9983000159263611,"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":0.9983000159263611,"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/T11476","display_name":"Graph theory and applications","score":0.9955000281333923,"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"}},{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.47545358538627625},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.412925660610199}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47545358538627625},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.412925660610199}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0963548324000269","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548324000269","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/861F9C17713FD1055F58598E6A4F058E/S0963548324000269a.pdf/div-class-title-a-note-on-extremal-constructions-for-the-erd-s-rademacher-problem-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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:187086","is_oa":true,"landing_page_url":"https://wrap.warwick.ac.uk/id/eprint/187086/1/maths-250724-wrap--revisedbyoleg.pdf","pdf_url":"https://wrap.warwick.ac.uk/id/eprint/187086/7/a-note-on-extremal-constructions-for-the-erdos-rademacher-problem.pdf","source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1017/s0963548324000269","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548324000269","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/861F9C17713FD1055F58598E6A4F058E/S0963548324000269a.pdf/div-class-title-a-note-on-extremal-constructions-for-the-erd-s-rademacher-problem-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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4403304347.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1555702583","https://openalex.org/W1607720736","https://openalex.org/W1851625382","https://openalex.org/W1971212574","https://openalex.org/W2011575706","https://openalex.org/W2019480324","https://openalex.org/W2049005199","https://openalex.org/W2078321205","https://openalex.org/W2087476504","https://openalex.org/W2108398244","https://openalex.org/W2166750439","https://openalex.org/W2312510043","https://openalex.org/W2323590783","https://openalex.org/W2743265602","https://openalex.org/W2949834637","https://openalex.org/W3014568888","https://openalex.org/W3098117341","https://openalex.org/W3103062633","https://openalex.org/W3129030546","https://openalex.org/W3212190075","https://openalex.org/W6786983727","https://openalex.org/W7014454993"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Abstract":[0],"For":[1],"given":[2],"positive":[3],"integers":[4],"$r\\ge":[5,47,114],"3$":[6,48],",":[7,12,49,60,120],"$n$":[8,29,51,119],"and":[9,31,38,116,127],"$e\\le":[10,58],"\\binom{n}{2}$":[11,59],"the":[13,19,41,88,96,107,122],"famous":[14],"Erd\u0151s\u2013Rademacher":[15],"problem":[16],"asks":[17],"for":[18,45,56,112],"minimum":[20,89],"number":[21,90],"of":[22,36,91,109,125],"$r$":[23,92],"-cliques":[24,93],"in":[25],"a":[26,70,76],"graph":[27,65,73,78],"with":[28],"vertices":[30],"$e$":[32],"edges.":[33],"A":[34],"conjecture":[35,124],"Lov\u00e1sz":[37],"Simonovits":[39],"from":[40,69],"1970s":[42],"states":[43],"that,":[44],"every":[46,57],"if":[50],"is":[52],"sufficiently":[53],"large":[54,118],"then,":[55],"at":[61],"least":[62],"one":[63,80],"extremal":[64,110],"can":[66],"be":[67,106],"obtained":[68],"complete":[71],"partite":[72],"by":[74,95],"adding":[75],"triangle-free":[77],"into":[79],"part.":[81],"In":[82],"this":[83],"note,":[84],"we":[85,100,103],"explicitly":[86],"write":[87],"predicted":[94],"above":[97],"conjecture.":[98],"Also,":[99],"describe":[101],"what":[102],"believe":[104],"to":[105],"set":[108],"graphs":[111],"any":[113],"4$":[115],"all":[117],"amending":[121],"previous":[123],"Pikhurko":[126],"Razborov.":[128]},"counts_by_year":[],"updated_date":"2026-06-14T06:11:07.267592","created_date":"2025-10-10T00:00:00"}