{"id":"https://openalex.org/W3111326342","doi":"https://doi.org/10.1137/18m1206126","title":"On the Number of Cliques in Graphs with a Forbidden Subdivision or Immersion","display_name":"On the Number of Cliques in Graphs with a Forbidden Subdivision or Immersion","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3111326342","doi":"https://doi.org/10.1137/18m1206126","mag":"3111326342"},"language":"en","primary_location":{"id":"doi:10.1137/18m1206126","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1206126","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/A5112361944","display_name":"Jacob Fox","orcid":"https://orcid.org/0000-0002-0664-497X"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jacob Fox","raw_affiliation_strings":["Department of Mathematics, Stanford University, Stanford, CA 94305"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Stanford University, Stanford, CA 94305","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100911449","display_name":"Fan Wei","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fan Wei","raw_affiliation_strings":["Department of Mathematics, Stanford University, Stanford, CA 94305"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Stanford University, Stanford, CA 94305","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112361944"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":2.1909,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.87650139,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"34","issue":"4","first_page":"2556","last_page":"2582"},"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":0.9990000128746033,"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":0.9970999956130981,"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":0.8631417751312256},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.782109797000885},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.6814725995063782},{"id":"https://openalex.org/keywords/substructure","display_name":"Substructure","score":0.5576425194740295},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5478883981704712},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5283178687095642},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47560176253318787},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47465211153030396},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.43753668665885925}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8631417751312256},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.782109797000885},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.6814725995063782},{"id":"https://openalex.org/C99679407","wikidata":"https://www.wikidata.org/wiki/Q56761637","display_name":"Substructure","level":2,"score":0.5576425194740295},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5478883981704712},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5283178687095642},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47560176253318787},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47465211153030396},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.43753668665885925},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","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/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1206126","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1206126","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":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.44999998807907104}],"awards":[{"id":"https://openalex.org/G1316152686","display_name":"CAREER: Extremal Combinatorics: Methods, Problems, and Challenges","funder_award_id":"1352121","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G308701274","display_name":null,"funder_award_id":"DMS-1352121","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306079","display_name":"David and Lucile Packard Foundation","ror":"https://ror.org/032atxq54"},{"id":"https://openalex.org/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1967546560","https://openalex.org/W1989340449","https://openalex.org/W2030012922","https://openalex.org/W2034838716","https://openalex.org/W2035763891","https://openalex.org/W2047993669","https://openalex.org/W2055049645","https://openalex.org/W2084389562","https://openalex.org/W2109542562","https://openalex.org/W2122404357","https://openalex.org/W2142101067","https://openalex.org/W2164875551","https://openalex.org/W2170758948","https://openalex.org/W2333921708","https://openalex.org/W2951014529","https://openalex.org/W2963651014","https://openalex.org/W2963779710","https://openalex.org/W3038100514"],"related_works":["https://openalex.org/W2153916713","https://openalex.org/W2023846184","https://openalex.org/W2384806462","https://openalex.org/W2703419385","https://openalex.org/W2329056228","https://openalex.org/W2284584236","https://openalex.org/W1979083399","https://openalex.org/W2375549870","https://openalex.org/W4244083562","https://openalex.org/W2296482608"],"abstract_inverted_index":{"How":[0],"many":[1],"cliques":[2,34,88],"can":[3],"a":[4,11,23,36,42],"graph":[5,37,56,92],"on":[6,38,57,107],"$n$":[7,39],"vertices":[8,40,61],"have":[9,19],"with":[10,41,62,93],"forbidden":[12,43],"substructure?":[13],"Extremal":[14],"problems":[15],"of":[16,33,87,133],"this":[17],"sort":[18],"been":[20],"studied":[21],"for":[22,50,101,129],"long":[24],"time.":[25],"This":[26,105],"paper":[27],"studies":[28],"the":[29,76,84,108,120],"maximum":[30,85],"possible":[31],"number":[32,86],"in":[35,89,131,135],"clique":[44],"subdivision":[45,134],"or":[46],"immersion.":[47],"We":[48,80,117],"prove":[49,82],"$t$":[51],"sufficiently":[52,102],"large":[53,103],"that":[54,83,119],"every":[55],"$n":[58],"\\geq":[59],"t$":[60],"no":[63,94],"$K_t$-immersion":[64],"has":[65],"at":[66,97],"most":[67,98],"$n2^{t+\\log_2^2":[68],"t}$":[69],"cliques,":[70],"which":[71],"is":[72,96,123],"sharp":[73],"apart":[74],"from":[75],"$2^{O(\\log^2":[77],"t)}$":[78],"factor.":[79],"also":[81],"an":[90],"$n$-vertex":[91],"$K_t$-subdivision":[95],"$2^{1.817t":[99],"}n$":[100],"$t$.":[104],"improves":[106],"best":[109],"known":[110],"exponential":[111],"constant":[112],"by":[113],"Lee":[114],"and":[115],"Oum.":[116],"conjecture":[118],"optimal":[121],"bound":[122],"$3^{2t/3":[124],"+o(t)}n$,":[125],"as":[126],"we":[127],"proved":[128],"minors":[130],"place":[132],"earlier":[136],"work.":[137]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
