Variable neighborhood search for extremal graphs. 5. Three ways to automate finding conjectures Original Research Article

The 2-color Rado number for the equation x1+x2−2x3=c, which for each constant c∈Z we denote by S1(c), is the least integer, if it exists, such that every 2-coloring, Δ : [1,S1(c)]→{0,1}, of the natural numbers admits a monochromatic solution to x1+x2−2x3=c, and otherwise S1(c)=∞. We determine the 2-color Rado number for the equation x1+x2−2x3=c, when additional inequality restraints on the variables are added. In particular, the case where we require x2