{"id":"https://openalex.org/W2072359115","doi":"https://doi.org/10.1137/10080868x","title":"More Constructive Lower Bounds on Classical Ramsey Numbers","display_name":"More Constructive Lower Bounds on Classical Ramsey Numbers","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2072359115","doi":"https://doi.org/10.1137/10080868x","mag":"2072359115"},"language":"en","primary_location":{"id":"doi:10.1137/10080868x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/10080868x","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/A5101988903","display_name":"Xiaodong Xu","orcid":"https://orcid.org/0000-0003-3370-8489"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaodong Xu","raw_affiliation_strings":["xxdmaths@sina.com#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"xxdmaths@sina.com#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012636371","display_name":"Zehui Shao","orcid":"https://orcid.org/0000-0003-0764-4135"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zehui Shao","raw_affiliation_strings":["kidszh_mail@163.com#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"kidszh_mail@163.com#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075568055","display_name":"Stanis\u0142aw Radziszowski","orcid":"https://orcid.org/0000-0002-1470-5517"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stanis\u0141aw P. Radziszowski","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8854,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.70588235,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"25","issue":"1","first_page":"394","last_page":"400"},"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":0.9995999932289124,"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":0.9995999932289124,"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":0.9986000061035156,"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":0.9933000206947327,"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":0.7594082355499268},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7480373382568359},{"id":"https://openalex.org/keywords/ramseys-theorem","display_name":"Ramsey's theorem","score":0.7220545411109924},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6765332818031311},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4561738967895508},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45523977279663086},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.387401282787323},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.052234143018722534},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.04509305953979492}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7594082355499268},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7480373382568359},{"id":"https://openalex.org/C44115641","wikidata":"https://www.wikidata.org/wiki/Q918099","display_name":"Ramsey's theorem","level":3,"score":0.7220545411109924},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6765332818031311},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4561738967895508},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45523977279663086},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.387401282787323},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.052234143018722534},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.04509305953979492},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/10080868x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/10080868x","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:10.1.1.174.6544","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.174.6544","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.rit.edu/%7Espr/PUBL/paper68.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W17284171","https://openalex.org/W1535728779","https://openalex.org/W1604945782","https://openalex.org/W1845405019","https://openalex.org/W2069905179","https://openalex.org/W2084021260","https://openalex.org/W2095689360","https://openalex.org/W2136503940","https://openalex.org/W2157632912","https://openalex.org/W2160738446","https://openalex.org/W2401037690","https://openalex.org/W4242364721"],"related_works":["https://openalex.org/W2963272825","https://openalex.org/W2036810061","https://openalex.org/W2149859310","https://openalex.org/W2891286913","https://openalex.org/W1966595665","https://openalex.org/W2582950667","https://openalex.org/W1969530432","https://openalex.org/W190077873","https://openalex.org/W4226451695","https://openalex.org/W2085740124"],"abstract_inverted_index":{"We":[0],"present":[1],"several":[2],"new":[3],"constructive":[4],"lower":[5,76],"bounds":[6,77],"for":[7,20,32,78],"classical":[8],"Ramsey":[9,79],"numbers.":[10],"In":[11],"particular,":[12],"the":[13,45,85],"inequality":[14],"$R(k,s+1)":[15],"\\geq":[16,22,39,43,58,60,63,92,95,98,101,104,107,110,113,116,119,122,130],"R(k,s)+2k-2$":[17],"is":[18,51],"proved":[19],"$k":[21,38,57,62],"5$.":[23],"The":[24],"general":[25],"construction":[26],"permits":[27],"us":[28],"to":[29],"prove":[30],"that,":[31],"all":[33],"integers":[34],"k,":[35,54],"l,":[36],"with":[37,84],"5$":[40],"and":[41,55,65,124],"$l":[42],"3$,":[44],"connectivity":[46],"of":[47,87],"any":[48],"Ramsey-critical":[49],"$(k,l)$-graph":[50],"at":[52],"least":[53],"if":[56],"l-1":[59],"1$,":[61],"3$":[64],"$(k,l)":[66],"\\neq":[67],"(3,2)$,":[68],"then":[69],"such":[70],"graphs":[71],"are":[72,81],"Hamiltonian.":[73],"New":[74],"concrete":[75],"numbers":[80],"obtained,":[82],"some":[83],"help":[86],"computer":[88],"algorithms,":[89],"including:":[90],"$R(5,17)":[91],"388$,":[93],"$R(5,19)":[94],"411$,":[96],"$R(5,20)":[97],"424$,":[99],"$R(6,8)":[100],"132$,":[102],"$R(6,12)":[103],"263$,":[105],"$R(7,8)":[106],"217$,":[108],"$R(7,9)":[109],"241$,":[111],"$R(7,12)":[112],"417$,":[114],"$R(8,17)":[115],"961$,":[117],"$R(9,10)":[118],"581$,":[120],"$R(12,12)":[121],"1639$,":[123],"also":[125],"one":[126],"three-color":[127],"case":[128],"$R(8,8,8)":[129],"6079$.":[131]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}