{"id":"https://openalex.org/W1987969576","doi":"https://doi.org/10.1137/s0895480101384086","title":"Asymptotic Size Ramsey Results for Bipartite Graphs","display_name":"Asymptotic Size Ramsey Results for Bipartite Graphs","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1987969576","doi":"https://doi.org/10.1137/s0895480101384086","mag":"1987969576"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480101384086","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480101384086","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/A5080095759","display_name":"Oleg Pikhurko","orcid":"https://orcid.org/0000-0002-9657-4011"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Oleg Pikhurko","raw_affiliation_strings":["Centre for Mathematical Sciences Cambridge University, Cambridge CB3 0WB, England"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Mathematical Sciences Cambridge University, Cambridge CB3 0WB, England","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080095759"],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":null,"apc_paid":null,"fwci":2.8109,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.89080119,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"16","issue":"1","first_page":"99","last_page":"113"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.989300012588501,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9890999794006348,"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":0.9040131568908691},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.8804746866226196},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8259186744689941},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6784276366233826},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6210544109344482},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5276564359664917},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.47267207503318787},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.4333406388759613},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4171592593193054},{"id":"https://openalex.org/keywords/ramsey-theory","display_name":"Ramsey theory","score":0.41216155886650085}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9040131568908691},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.8804746866226196},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8259186744689941},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6784276366233826},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6210544109344482},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5276564359664917},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.47267207503318787},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.4333406388759613},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4171592593193054},{"id":"https://openalex.org/C112291201","wikidata":"https://www.wikidata.org/wiki/Q1336170","display_name":"Ramsey theory","level":2,"score":0.41216155886650085},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0895480101384086","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480101384086","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.234.5339","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.5339","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/math/0101197v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.235.2297","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.2297","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/math/0101197v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.26.4836","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.26.4836","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.pmms.cam.ac.uk/~oleg/siambip.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1995186677","https://openalex.org/W2021319109","https://openalex.org/W2037949852","https://openalex.org/W2068593598","https://openalex.org/W2092778349","https://openalex.org/W2126442385","https://openalex.org/W2164302265","https://openalex.org/W2751866474","https://openalex.org/W4205528879","https://openalex.org/W4241497605"],"related_works":["https://openalex.org/W2091826982","https://openalex.org/W245205139","https://openalex.org/W2036057584","https://openalex.org/W4246000090","https://openalex.org/W2107875203","https://openalex.org/W4234658180","https://openalex.org/W4235849992","https://openalex.org/W2910933086","https://openalex.org/W3143578817","https://openalex.org/W4288630335"],"abstract_inverted_index":{"We":[0],"show":[1,65],"that":[2,142],"$\\lim_{n\\to\\infty}\\hat":[3],"r(F_{1,n},\\dots,F_{q,n},F_{q+1},\\dots,F_{r})/n$":[4],"exists,":[5],"where":[6],"the":[7,49,52,61,82,100,119],"bipartite":[8,26,77],"graphs":[9],"$F_{q+1},\\dots,F_r$":[10],"do":[11],"not":[12],"depend":[13],"on":[14],"n":[15],"while,":[16],"for":[17,41,99,105],"$1\\le":[18],"i\\le":[19],"q$,":[20],"$F_{i,n}$":[21],"is":[22,51,74],"obtained":[23],"from":[24],"some":[25,42],"graph":[27,73],"$F_i$":[28],"with":[29],"parts":[30],"$V_1\\cup":[31],"V_2=V(F_i)$":[32],"by":[33],"duplicating":[34],"each":[35,71],"vertex":[36],"$v\\in":[37],"V_2$":[38],"$(c_v+o(1))n$":[39],"times":[40],"real":[43],"$c_v":[44],">":[45],"0$.":[46],"In":[47],"fact,":[48],"limit":[50],"minimum":[53],"of":[54,84,102,121],"a":[55,75],"certain":[56],"mixed":[57],"integer":[58],"program.":[59],"Using":[60],"Farkas":[62],"lemma":[63],"we":[64,112],"how":[66],"to":[67],"compute":[68],"it":[69],"when":[70],"forbidden":[72],"complete":[76],"graph,":[78],"in":[79,126],"particular":[80],"answering":[81],"question":[83],"Erdos,":[85],"Faudree,":[86,122],"Rousseau,":[87,123],"and":[88,108,124,129],"Schelp":[89],"[Period.\\":[90],"Math.\\":[91],"Hungar.,":[92],"9":[93],"(1978),":[94],"pp.":[95,140],"145--161],":[96],"who":[97],"asked":[98],"asymptotics":[101],"$\\hat":[103,143],"r(K_{s,n},K_{s,n})$":[104],"fixed":[106],"s":[107],"large":[109,117],"n.":[110],"Also,":[111],"prove":[113],"(for":[114],"all":[115],"sufficiently":[116],"n)":[118],"conjecture":[120],"Sheehan":[125],"[Graph":[127],"Theory":[128],"Combinatorics,":[130],"B.":[131],"Bollobas,":[132],"ed.,":[133],"Cambridge":[134],"University":[135],"Press,":[136],"Cambridge,":[137],"UK,":[138],"1984,":[139],"273--281]":[141],"r(K_{2,n},K_{2,n})":[144],"=18n-15$.":[145]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}