List \(T\)-colorings of graphs (Q1309815)

Given a set \(T\) and an integer \(k\), a graph \(G\) is \(T-k\) choosable if, for every assignment of (possibly different) lists of \(k\) integers to the vertices of \(G\), there exists a \(T\)-colouring of \(G\) colouring each vertex with an element from the list assigned to that vertex. Exact values and bounds on the smallest \(k\) needed to be \(T-k\) choosable are presented for chordal graphs, complete (bipartite) graphs, trees and \(T\) sets. \(T-k\) choosability has highly interesting applications in radio and television frequency assignment.