Off-diagonal Rado number for x+y+c=z and x+qy=z
Year: 2026
Type: article
Abstract: Ramsey-type problems for linear equations began with Schur’s theorem and were systematically generalized by Richard Rado. In the off-diagonal framework for two colors, one considers two different linear equations ( E 1 , E 2 ) and determines the minimum integer N for which any red–blue coloring of { 1,2 , … , N } forces either a red solution of the equation E 1 or a blue solution of the equation E 2 . In this work, we study the off-diagonal Rado numbers for a combination of homogeneous and non-homogeneous linear equations of the forms x + y + c = z and x + q y = z . We determine the exact two-color off-diagonal Rado number, denoted as R 2 ( c , q ) , associated with this system of equations.
Source: Discrete Applied Mathematics
Institution: Indian Institute of Science Bangalore
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W7133237201
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