{"id":"https://openalex.org/W3000265346","doi":"https://doi.org/10.37236/7343","title":"Many Triangles with Few Edges","display_name":"Many Triangles with Few Edges","publication_year":2019,"publication_date":"2019-05-31","ids":{"openalex":"https://openalex.org/W3000265346","doi":"https://doi.org/10.37236/7343","mag":"3000265346"},"language":"en","primary_location":{"id":"doi:10.37236/7343","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7343","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p36/7850","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p36/7850","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064804027","display_name":"Rachel Kirsch","orcid":"https://orcid.org/0000-0002-6633-3444"},"institutions":[{"id":"https://openalex.org/I909854389","display_name":"London School of Economics and Political Science","ror":"https://ror.org/0090zs177","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I909854389"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Rachel Kirsch","raw_affiliation_strings":["London School of Economics and Political Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"London School of Economics and Political Sciences","institution_ids":["https://openalex.org/I909854389"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032520716","display_name":"A. J. Radcliffe","orcid":"https://orcid.org/0000-0002-8817-0383"},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. J. Radcliffe","raw_affiliation_strings":["University of Nebraska-Lincoln"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Nebraska-Lincoln","institution_ids":["https://openalex.org/I114395901"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.3638,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.96891711,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"26","issue":"2","first_page":null,"last_page":null},"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":0.9997000098228455,"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":0.9997000098228455,"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":0.996399998664856,"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/T11476","display_name":"Graph theory and applications","score":0.9829000234603882,"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":0.9213764667510986},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8155957460403442},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7834354639053345},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5757114887237549},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.514043927192688},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38838332891464233},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06354185938835144}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9213764667510986},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8155957460403442},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7834354639053345},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5757114887237549},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.514043927192688},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38838332891464233},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06354185938835144},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/7343","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7343","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p36/7850","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/7343","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7343","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p36/7850","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3000265346.pdf","grobid_xml":"https://content.openalex.org/works/W3000265346.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W2011504778","https://openalex.org/W2074614998","https://openalex.org/W2076871859","https://openalex.org/W2087239176","https://openalex.org/W2115164934","https://openalex.org/W2125820980","https://openalex.org/W2144467924","https://openalex.org/W2149047110","https://openalex.org/W2211407870","https://openalex.org/W2229409480","https://openalex.org/W2964242048","https://openalex.org/W3105673126","https://openalex.org/W3124913715","https://openalex.org/W3136243343","https://openalex.org/W6688556463","https://openalex.org/W6758373158","https://openalex.org/W6786275054"],"related_works":["https://openalex.org/W3161230432","https://openalex.org/W1487201914","https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W2784911598","https://openalex.org/W4367190712","https://openalex.org/W280458463","https://openalex.org/W4297950433","https://openalex.org/W1170131723"],"abstract_inverted_index":{"Extremal":[0],"problems":[1],"concerning":[2],"the":[3,50,71,111,117,131,138],"number":[4,52,72,112,118,139],"of":[5,53,59,73,105,113,116,119,140],"independent":[6],"sets":[7],"or":[8],"complete":[9,54,74],"subgraphs":[10,75],"in":[11,18],"a":[12,57,103,157],"graph":[13,133],"have":[14],"been":[15],"well":[16],"studied":[17],"recent":[19],"years.":[20],"Cutler":[21,91],"and":[22,31,41,63,84,92,147,161],"Radcliffe":[23,93],"proved":[24,85,94],"that":[25,66,123],"among":[26,142],"graphs":[27,143],"with":[28,144],"$n$":[29],"vertices":[30],"maximum":[32,51,150],"degree":[33,151],"at":[34],"most":[35],"$r$,":[36],"where":[37,108,127,154],"$n":[38],"=":[39,89,156],"a(r+1)+b$":[40],"$0":[42,162],"\\le":[43,45,99,163],"b":[44,164],"r$,":[46],"$aK_{r+1}\\cup":[47,67,124],"K_b$":[48,68],"has":[49],"subgraphs,":[55],"answering":[56],"question":[58],"Galvin.":[60],"Gan,":[61],"Loh,":[62],"Sudakov":[64],"conjectured":[65],"also":[69],"maximizes":[70,137],"$K_t$":[76],"for":[77,87,97],"each":[78],"fixed":[79,149],"size":[80],"$t":[81],"\\ge":[82],"3$,":[83],"this":[86,95,106],"$a":[88],"1$.":[90],"conjecture":[96],"$r":[98],"6$.":[100],"We":[101,121],"investigate":[102],"variant":[104],"problem":[107],"we":[109],"fix":[110],"edges":[114,146],"instead":[115],"vertices.":[120],"prove":[122],"{\\mathcal":[125],"C}(b)$,":[126],"${\\mathcal":[128],"C}(b)$":[129],"is":[130],"colex":[132],"on":[134],"$b$":[135],"edges,":[136],"triangles":[141],"$m$":[145],"any":[148],"$r\\le":[152],"8$,":[153],"$m":[155],"\\binom{r+1}{2}":[158],"+":[159],"b$":[160],"&lt;":[165],"\\binom{r+1}{2}$.":[166]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
