{"id":"https://openalex.org/W2024157339","doi":"https://doi.org/10.1016/s0012-365x(99)00137-5","title":"On some generalizations of the van der Waerden number w(3)","display_name":"On some generalizations of the van der Waerden number w(3)","publication_year":1999,"publication_date":"1999-09-01","ids":{"openalex":"https://openalex.org/W2024157339","doi":"https://doi.org/10.1016/s0012-365x(99)00137-5","mag":"2024157339"},"language":"en","primary_location":{"id":"doi:10.1016/s0012-365x(99)00137-5","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(99)00137-5","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"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/A5111560401","display_name":"Bruce Landman","orcid":null},"institutions":[{"id":"https://openalex.org/I169335092","display_name":"University of North Carolina at Greensboro","ror":"https://ror.org/04fnxsj42","country_code":"US","type":"education","lineage":["https://openalex.org/I169335092"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Bruce M. Landman","raw_affiliation_strings":["Department of Mathematical Sciences, University of North Carolina at Greensboro, P.O. Box 26170 Greensboro, NC 27402-6170, USA","Department of Mathematical Sciences, University of North Carolina at Greensboro, P.O. Box 26170, Greensboro, NC 27402-6170, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of North Carolina at Greensboro, P.O. Box 26170 Greensboro, NC 27402-6170, USA","institution_ids":["https://openalex.org/I169335092"]},{"raw_affiliation_string":"Department of Mathematical Sciences, University of North Carolina at Greensboro, P.O. Box 26170, Greensboro, NC 27402-6170, USA","institution_ids":["https://openalex.org/I169335092"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111560401"],"corresponding_institution_ids":["https://openalex.org/I169335092"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":0.5909,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.61747851,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"207","issue":"1-3","first_page":"137","last_page":"147"},"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":0.9779000282287598,"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":0.9779000282287598,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9711999893188477,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9293000102043152,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.8634476661682129},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.861124575138092},{"id":"https://openalex.org/keywords/van-der-waerdens-theorem","display_name":"Van der Waerden's theorem","score":0.8575010299682617},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.741773784160614},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6943787336349487},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5541417598724365},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.548158586025238},{"id":"https://openalex.org/keywords/monochromatic-color","display_name":"Monochromatic color","score":0.4766598343849182},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4737613797187805},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40241482853889465},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05883219838142395}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8634476661682129},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.861124575138092},{"id":"https://openalex.org/C116493835","wikidata":"https://www.wikidata.org/wiki/Q764287","display_name":"Van der Waerden's theorem","level":2,"score":0.8575010299682617},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.741773784160614},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6943787336349487},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5541417598724365},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.548158586025238},{"id":"https://openalex.org/C40833965","wikidata":"https://www.wikidata.org/wiki/Q6901438","display_name":"Monochromatic color","level":2,"score":0.4766598343849182},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4737613797187805},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40241482853889465},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05883219838142395},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0012-365x(99)00137-5","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(99)00137-5","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2391021702","https://openalex.org/W1987972399","https://openalex.org/W2890157477","https://openalex.org/W2033895221","https://openalex.org/W2025456998","https://openalex.org/W2953008743","https://openalex.org/W2417925590","https://openalex.org/W2293174673","https://openalex.org/W4298180898","https://openalex.org/W2079849989"],"abstract_inverted_index":null,"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}