Article
Exact value of 3 color weak Rado number
Author/s | Revuelta Marchena, María Pastora
![]() ![]() ![]() ![]() ![]() ![]() ![]() Boza Prieto, Luis ![]() ![]() ![]() ![]() Marín Sánchez, Juan Manuel Sanz Domínguez, María Isabel |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2016 |
Deposit Date | 2022-09-01 |
Published in |
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Abstract | For integers k, n, c with k, n ≥ 1 and c ≥ 0, the n color weak Rado number
W Rk(n, c) is defined as the least integer N, if it exists, such that for every n coloring of the set {1, 2, ..., N}, there exists a monochromatic ... For integers k, n, c with k, n ≥ 1 and c ≥ 0, the n color weak Rado number W Rk(n, c) is defined as the least integer N, if it exists, such that for every n coloring of the set {1, 2, ..., N}, there exists a monochromatic solution in that set to the equation x1 + x2 + ... + xk + c = xk+1, such that xi = xj when i = j. If no such N exists, then W Rk(n, c) is defined as infinite. In this work, we consider the main issue regarding the 3 color weak Rado number for the equation x1 + x2 + c = x3 and the exact value of the W R2(3, c) = 13c + 22 is established. |
Citation | Revuelta Marchena, M.P., Boza Prieto, L., Marín, J.M. y Sanz, M.I. (2016). Exact value of 3 color weak Rado number. Electronic Notes in Discrete Mathematics, 54 (October 2016), 241-245. |
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