{"id":"https://openalex.org/W2301495908","doi":"https://doi.org/10.1017/s0963548313000448","title":"Short Proofs of Some Extremal Results","display_name":"Short Proofs of Some Extremal Results","publication_year":2013,"publication_date":"2013-11-04","ids":{"openalex":"https://openalex.org/W2301495908","doi":"https://doi.org/10.1017/s0963548313000448","mag":"2301495908"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548313000448","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548313000448","pdf_url":null,"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":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/1721.1/92861","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042722711","display_name":"David Conlon","orcid":"https://orcid.org/0000-0001-5899-1829"},"institutions":[{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]},{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["SK","US"],"is_corresponding":true,"raw_author_name":"DAVID CONLON","raw_affiliation_strings":["Mathematical Institute, Oxford OX1 3LB, UK (e-mail:","Mathematical Institute, Oxford OX1 3LB, UK","Department of Mathematics, MIT, Cambridge, MA 02139-4307, USA"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, Oxford OX1 3LB, UK (e-mail:","institution_ids":["https://openalex.org/I4210120676"]},{"raw_affiliation_string":"Mathematical Institute, Oxford OX1 3LB, UK","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, MIT, Cambridge, MA 02139-4307, USA","institution_ids":["https://openalex.org/I4210110987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112361944","display_name":"Jacob Fox","orcid":"https://orcid.org/0000-0002-0664-497X"},"institutions":[{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"JACOB FOX","raw_affiliation_strings":["Department of Mathematics, MIT, Cambridge, MA 02139-4307, USA (e-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, MIT, Cambridge, MA 02139-4307, USA (e-mail:","institution_ids":["https://openalex.org/I4210110987"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066741544","display_name":"Benny Sudakov","orcid":"https://orcid.org/0000-0003-3307-9475"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"BENNY SUDAKOV","raw_affiliation_strings":["Department of Mathematics, UCLA, Los Angeles, CA 90095, USA (e-mail:","Department of Mathematics, UCLA, Los Angeles, CA 90095, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, CA 90095, USA (e-mail:","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, CA 90095, USA","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5042722711"],"corresponding_institution_ids":["https://openalex.org/I4210110987","https://openalex.org/I4210120676"],"apc_list":null,"apc_paid":null,"fwci":3.3822,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.91499729,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"23","issue":"1","first_page":"8","last_page":"28"},"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":0.9983000159263611,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9943000078201294,"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/mathematical-proof","display_name":"Mathematical proof","score":0.9181139469146729},{"id":"https://openalex.org/keywords/extremal-combinatorics","display_name":"Extremal combinatorics","score":0.8268513679504395},{"id":"https://openalex.org/keywords/extremal-graph-theory","display_name":"Extremal graph theory","score":0.7710690498352051},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6655434370040894},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6393396854400635},{"id":"https://openalex.org/keywords/ramsey-theory","display_name":"Ramsey theory","score":0.5546311140060425},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5131908059120178},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.4829941987991333},{"id":"https://openalex.org/keywords/enumerative-combinatorics","display_name":"Enumerative combinatorics","score":0.45535117387771606},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43667834997177124},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.061114728450775146},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.06014636158943176}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.9181139469146729},{"id":"https://openalex.org/C549619432","wikidata":"https://www.wikidata.org/wiki/Q5422299","display_name":"Extremal combinatorics","level":2,"score":0.8268513679504395},{"id":"https://openalex.org/C12595997","wikidata":"https://www.wikidata.org/wiki/Q739245","display_name":"Extremal graph theory","level":5,"score":0.7710690498352051},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6655434370040894},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6393396854400635},{"id":"https://openalex.org/C112291201","wikidata":"https://www.wikidata.org/wiki/Q1336170","display_name":"Ramsey theory","level":2,"score":0.5546311140060425},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5131908059120178},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.4829941987991333},{"id":"https://openalex.org/C112497148","wikidata":"https://www.wikidata.org/wiki/Q336787","display_name":"Enumerative combinatorics","level":2,"score":0.45535117387771606},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43667834997177124},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.061114728450775146},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.06014636158943176},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1017/s0963548313000448","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548313000448","pdf_url":null,"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:authors.library.caltech.edu:97805","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20190812-162956937","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.712.6998","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.712.6998","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.maths.ox.ac.uk/%7Econlond/essays.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.752.7135","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.752.7135","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1212.1300.pdf","raw_type":"text"},{"id":"pmh:oai:dspace.mit.edu:1721.1/92861","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/92861","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv","raw_type":"http://purl.org/eprint/type/JournalArticle"}],"best_oa_location":{"id":"pmh:oai:dspace.mit.edu:1721.1/92861","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/92861","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv","raw_type":"http://purl.org/eprint/type/JournalArticle"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W71100071","https://openalex.org/W648165475","https://openalex.org/W1494890830","https://openalex.org/W1524397983","https://openalex.org/W1547514922","https://openalex.org/W1646261625","https://openalex.org/W1758827340","https://openalex.org/W1839512959","https://openalex.org/W1966321066","https://openalex.org/W1970804184","https://openalex.org/W1976762380","https://openalex.org/W1980392837","https://openalex.org/W1984962604","https://openalex.org/W1989751882","https://openalex.org/W1996516812","https://openalex.org/W1998568320","https://openalex.org/W2001172982","https://openalex.org/W2001765932","https://openalex.org/W2004294976","https://openalex.org/W2004458705","https://openalex.org/W2005870935","https://openalex.org/W2007400275","https://openalex.org/W2014956840","https://openalex.org/W2015922523","https://openalex.org/W2022675369","https://openalex.org/W2025085400","https://openalex.org/W2037159051","https://openalex.org/W2052019697","https://openalex.org/W2060194042","https://openalex.org/W2065634598","https://openalex.org/W2072242470","https://openalex.org/W2072548859","https://openalex.org/W2077213922","https://openalex.org/W2093480133","https://openalex.org/W2095689360","https://openalex.org/W2114933597","https://openalex.org/W2116453796","https://openalex.org/W2121456457","https://openalex.org/W2126793513","https://openalex.org/W2127163760","https://openalex.org/W2131309366","https://openalex.org/W2131312475","https://openalex.org/W2132134025","https://openalex.org/W2135737379","https://openalex.org/W2137669983","https://openalex.org/W2144725195","https://openalex.org/W2162218992","https://openalex.org/W2254576550","https://openalex.org/W3004234532","https://openalex.org/W3083309575","https://openalex.org/W3083502596","https://openalex.org/W3100937370","https://openalex.org/W3104854165","https://openalex.org/W4214858939","https://openalex.org/W4234919473","https://openalex.org/W4242102268","https://openalex.org/W4253428136","https://openalex.org/W4285719527","https://openalex.org/W6632787053"],"related_works":["https://openalex.org/W3004234532","https://openalex.org/W2093480133","https://openalex.org/W2935028240","https://openalex.org/W3146129092","https://openalex.org/W265966088","https://openalex.org/W2282824953","https://openalex.org/W4238271946","https://openalex.org/W4299647868","https://openalex.org/W2523626070","https://openalex.org/W562159316"],"abstract_inverted_index":{"We":[0],"prove":[1],"several":[2],"results":[3],"from":[4,24],"different":[5],"areas":[6,25],"of":[7,18],"extremal":[8,28],"combinatorics,":[9,35],"giving":[10],"complete":[11],"or":[12],"partial":[13],"solutions":[14],"to":[15],"a":[16],"number":[17],"open":[19],"problems.":[20],"These":[21],"results,":[22],"coming":[23],"such":[26],"as":[27],"graph":[29],"theory,":[30],"Ramsey":[31],"theory":[32],"and":[33],"additive":[34],"have":[36],"been":[37],"collected":[38],"together":[39],"because":[40],"in":[41],"each":[42],"case":[43],"the":[44],"relevant":[45],"proofs":[46],"are":[47],"quite":[48],"short.":[49]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}