Two-color Rado number of x plus y plus c = kz for odd c and k with k >= c+6
DC Field | Value | Language |
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dc.contributor.author | Kim, Byeong Moon | - |
dc.contributor.author | Hwang, Woonjae | - |
dc.contributor.author | Song, Byung Chul | - |
dc.date.accessioned | 2022-11-19T16:41:10Z | - |
dc.date.available | 2022-11-19T16:41:10Z | - |
dc.date.created | 2022-11-17 | - |
dc.date.issued | 2022-03 | - |
dc.identifier.issn | 0012-365X | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/145963 | - |
dc.description.abstract | For positive integers c and k, 2-color Rado number R = R(c, k) is the least integer, provided it exists, such that every 2-coloring of the positive integers up to R admits a monochromatic solution to x + y + c = kz. It is known that R exists if and only if k is odd or c is even. In this paper, for odd c, k we show that R(c, k) = 1/2(k(k + 1) - c + 1) when k >= c + 6. Moreover, we show that 1/2(k(k +1) - c +1) is also an upper bound of R(c, k) when k >= c + 4. (C) 2021 Elsevier B.V. All rights reserved. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | ELSEVIER | - |
dc.title | Two-color Rado number of x plus y plus c = kz for odd c and k with k >= c+6 | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Hwang, Woonjae | - |
dc.identifier.doi | 10.1016/j.disc.2021.112750 | - |
dc.identifier.scopusid | 2-s2.0-85120944253 | - |
dc.identifier.wosid | 000819848100011 | - |
dc.identifier.bibliographicCitation | DISCRETE MATHEMATICS, v.345, no.3 | - |
dc.relation.isPartOf | DISCRETE MATHEMATICS | - |
dc.citation.title | DISCRETE MATHEMATICS | - |
dc.citation.volume | 345 | - |
dc.citation.number | 3 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordAuthor | Rado number | - |
dc.subject.keywordAuthor | Schur number | - |
dc.subject.keywordAuthor | Coloring | - |
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