T-choosability in Graphs

Given a set of nonnegative integers T , and a function S which assigns a set of integers S(v) to each vertex v of a graph G, an S-list T -coloring c of G is a vertexcoloring (with positive integers) of G such that c(v) 2 S(v) whenever v 2 V (G) andjc(u) c(w)j62 T whenever (u;w)2 E(G). For a xed T , the T -choice number