A rainbow about \(T\)-colorings for complete graphs (Q1918544)

By a \(T\)-colouring of a graph \(G= (V, E)\) we mean a function \(f: V\to N_0\) such that \(|f(x)- f(y)|\) does not belong to \(T\) for each \(xy\in E\), where \(T\) is a finite set of positive integers with 0. \(T\)-span of \(G\) is the minimum span over all \(T\)-colourings of \(G\). The \(T\)-span of a complete graph is shown to be NP-complete.