A rainbow about T-colorings for complete graphs

Abstract

Given a finite set T of positive integers, with 0 ϵ T, a T-coloring of a graph G = ( V, E) is a function f: V → N 0 such that for each { x, y} ϵE| f( x) − f( y)|∉ T. The T-span is the difference between the largest and smallest colors and the T-span of G is the minimum span over all T-colorings of G. We show that the problem to find the T-span for a complete graph is NP-complete.