{"id":"https://openalex.org/W2885953344","doi":"https://doi.org/10.37236/8085","title":"Off-Diagonal Ordered Ramsey Numbers of Matchings","display_name":"Off-Diagonal Ordered Ramsey Numbers of Matchings","publication_year":2019,"publication_date":"2019-05-17","ids":{"openalex":"https://openalex.org/W2885953344","doi":"https://doi.org/10.37236/8085","mag":"2885953344"},"language":"en","primary_location":{"id":"doi:10.37236/8085","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8085","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p21/7834","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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p21/7834","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036102061","display_name":"Dhruv Rohatgi","orcid":"https://orcid.org/0000-0002-0569-6698"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dhruv Rohatgi","raw_affiliation_strings":["Massachusetts Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5036102061"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07267922,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"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":0.9998999834060669,"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":0.9965000152587891,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9911999702453613,"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":0.9110924005508423},{"id":"https://openalex.org/keywords/ramseys-theorem","display_name":"Ramsey's theorem","score":0.7780818939208984},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7008804082870483},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6867628693580627},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.575946033000946},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5591602921485901},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.47390925884246826},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.45599526166915894},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4235481321811676},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3765684962272644},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37034013867378235},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13716694712638855}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9110924005508423},{"id":"https://openalex.org/C44115641","wikidata":"https://www.wikidata.org/wiki/Q918099","display_name":"Ramsey's theorem","level":3,"score":0.7780818939208984},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7008804082870483},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6867628693580627},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.575946033000946},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5591602921485901},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.47390925884246826},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.45599526166915894},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4235481321811676},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3765684962272644},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37034013867378235},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13716694712638855},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/8085","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8085","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p21/7834","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"},{"id":"pmh:oai:arXiv.org:1808.04025","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.04025","pdf_url":"https://arxiv.org/pdf/1808.04025","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2885953344","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1808.04025v1","pdf_url":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1808.04025","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1808.04025","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/8085","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8085","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p21/7834","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/W2885953344.pdf","grobid_xml":"https://content.openalex.org/works/W2885953344.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W281915830","https://openalex.org/W1487872891","https://openalex.org/W2074920973","https://openalex.org/W2095689360","https://openalex.org/W6610084081","https://openalex.org/W6669450416","https://openalex.org/W6766483811"],"related_works":["https://openalex.org/W3000486299","https://openalex.org/W1493361730","https://openalex.org/W3204532083","https://openalex.org/W2768930897","https://openalex.org/W2982522950","https://openalex.org/W2621541822","https://openalex.org/W2090526201","https://openalex.org/W2311250512","https://openalex.org/W2914209556","https://openalex.org/W2810413867","https://openalex.org/W1582237054","https://openalex.org/W1500875818","https://openalex.org/W2911850936","https://openalex.org/W3207998522","https://openalex.org/W2340026689","https://openalex.org/W2967508960","https://openalex.org/W2106970948","https://openalex.org/W2141063223","https://openalex.org/W2950098404","https://openalex.org/W2969799327"],"abstract_inverted_index":{"For":[0],"ordered":[1,7,24,67,76,105,147,163,167,188],"graphs":[2],"$G$":[3,35],"and":[4,62,126],"$H$,":[5,41],"the":[6,12,22,43,47,65,100,119,161],"Ramsey":[8,68,164],"number":[9,53,69,193],"$r_&lt;(G,H)$":[10],"is":[11,64,74,102,115,123,133],"smallest":[13],"$n$":[14,79,109],"such":[15,139],"that":[16,131,140,160],"every":[17,146],"red/blue":[18],"edge":[19],"coloring":[20],"of":[21,34,40,50,54,155],"complete":[23],"graph":[25],"on":[26,78,108],"vertices":[27],"$\\{1,\\dots,n\\}$":[28],"contains":[29],"either":[30],"a":[31,37,181],"blue":[32],"copy":[33,39],"or":[36],"red":[38],"where":[42,72,99],"embedding":[44],"must":[45],"preserve":[46],"relative":[48],"order":[49],"vertices.":[51,80,110],"One":[52],"interest,":[55],"first":[56],"studied":[57],"by":[58],"Conlon,":[59],"Fox,":[60],"Lee,":[61],"Sudakov,":[63],"off-diagonal":[66,162],"$r_&lt;(M,":[70,141],"K_3)$,":[71,98],"$M$":[73,107],"an":[75],"matching":[77,148],"In":[81],"particular,":[82],"Conlon":[83,127],"et":[84,128],"al.":[85,129],"asked":[86],"what":[87],"asymptotic":[88],"bounds":[89],"(in":[90],"$n$)":[91],"can":[92],"be":[93],"obtained":[94],"for":[95,145,166,186],"$\\max":[96],"r_&lt;(M,":[97],"maximum":[101],"over":[103],"all":[104],"matchings":[106,168,189],"The":[111],"best-known":[112,120],"upper":[113,184],"bound":[114,122,185],"$O(n^2/\\log":[116],"n)$,":[117],"whereas":[118],"lower":[121],"$\\Omega((n/\\log":[124],"n)^{4/3})$,":[125],"hypothesize":[130],"there":[132],"some":[134],"fixed":[135],"$\\epsilon":[136],"&gt;":[137],"0$":[138],"K_3)":[142],"=":[143],"O(n^{2-\\epsilon})$":[144],"$M$.":[149],"We":[150,158,178],"resolve":[151],"two":[152],"special":[153],"cases":[154],"this":[156],"conjecture.":[157],"show":[159],"numbers":[165],"in":[169],"which":[170],"edges":[171],"do":[172],"not":[173],"cross":[174],"are":[175],"nearly":[176],"linear.":[177],"also":[179],"prove":[180],"truly":[182],"sub-quadratic":[183],"random":[187],"with":[190],"interval":[191],"chromatic":[192],"$2$.":[194]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
