{"id":"https://openalex.org/W7118184598","doi":"https://doi.org/10.1007/s00373-025-03009-1","title":"Two and Three-color Rado numbers for $$x_1+x_2+\\cdots +x_n=y^2$$","display_name":"Two and Three-color Rado numbers for $$x_1+x_2+\\cdots +x_n=y^2$$","publication_year":2026,"publication_date":"2026-01-05","ids":{"openalex":"https://openalex.org/W7118184598","doi":"https://doi.org/10.1007/s00373-025-03009-1"},"language":"en","primary_location":{"id":"doi:10.1007/s00373-025-03009-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00373-025-03009-1","pdf_url":null,"source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","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/A5050049471","display_name":"Byeong Moon Kim","orcid":"https://orcid.org/0000-0001-6924-268X"},"institutions":[{"id":"https://openalex.org/I133533813","display_name":"Gangneung\u2013Wonju National University","ror":"https://ror.org/0461cvh40","country_code":"KR","type":"education","lineage":["https://openalex.org/I133533813"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Byeong Moon Kim","raw_affiliation_strings":["Department of Mathematics, Gangneung-Wonju National University, Gangneung, 25457, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Gangneung-Wonju National University, Gangneung, 25457, Korea","institution_ids":["https://openalex.org/I133533813"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112765292","display_name":"Byung Chul Song","orcid":null},"institutions":[{"id":"https://openalex.org/I133533813","display_name":"Gangneung\u2013Wonju National University","ror":"https://ror.org/0461cvh40","country_code":"KR","type":"education","lineage":["https://openalex.org/I133533813"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Byung Chul Song","raw_affiliation_strings":["Department of Mathematics, Gangneung-Wonju National University, Gangneung, 25457, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Gangneung-Wonju National University, Gangneung, 25457, Korea","institution_ids":["https://openalex.org/I133533813"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023980866","display_name":"Woonjae Hwang","orcid":null},"institutions":[{"id":"https://openalex.org/I28777354","display_name":"Sejong University","ror":"https://ror.org/00aft1q37","country_code":"KR","type":"education","lineage":["https://openalex.org/I28777354"]},{"id":"https://openalex.org/I4210124601","display_name":"Department of Mathematical Sciences","ror":"https://ror.org/02xkdev90","country_code":"RU","type":"government","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210124601"]}],"countries":["KR","RU"],"is_corresponding":true,"raw_author_name":"Woonjae Hwang","raw_affiliation_strings":["Division of Applied Mathematical Sciences, Korea University, Sejong, 30019, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematical Sciences, Korea University, Sejong, 30019, Korea","institution_ids":["https://openalex.org/I28777354","https://openalex.org/I4210124601"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023980866"],"corresponding_institution_ids":["https://openalex.org/I28777354","https://openalex.org/I4210124601"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0513403,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"42","issue":"1","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":0.9516000151634216,"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":0.9516000151634216,"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":0.01080000028014183,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.009800000116229057,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6158999800682068},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5514000058174133},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43479999899864197},{"id":"https://openalex.org/keywords/monochromatic-color","display_name":"Monochromatic color","score":0.41690000891685486},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.41589999198913574}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8719000220298767},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8504999876022339},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6158999800682068},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5514000058174133},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4462999999523163},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43479999899864197},{"id":"https://openalex.org/C40833965","wikidata":"https://www.wikidata.org/wiki/Q6901438","display_name":"Monochromatic color","level":2,"score":0.41690000891685486},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.41589999198913574},{"id":"https://openalex.org/C199879729","wikidata":"https://www.wikidata.org/wiki/Q205140","display_name":"Infinite set","level":3,"score":0.25760000944137573},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.25189998745918274},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00373-025-03009-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00373-025-03009-1","pdf_url":null,"source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1215584041","display_name":null,"funder_award_id":"RS-2023-00247457","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G4359381801","display_name":null,"funder_award_id":"RS-2023-00256221","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W50207286","https://openalex.org/W1490170438","https://openalex.org/W1597720546","https://openalex.org/W1957100706","https://openalex.org/W1970462267","https://openalex.org/W1998184029","https://openalex.org/W2030488028","https://openalex.org/W2040485991","https://openalex.org/W2057739679","https://openalex.org/W2064240737","https://openalex.org/W2070496958","https://openalex.org/W2076660932","https://openalex.org/W2115038771","https://openalex.org/W2210568818","https://openalex.org/W2511723084","https://openalex.org/W2904524109","https://openalex.org/W2990268793","https://openalex.org/W4200241270","https://openalex.org/W4289816080","https://openalex.org/W4385541298","https://openalex.org/W4400459896"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2026-01-05T00:00:00"}