The concept of list coloring and choosability was introduced in the seventies independently by Vizing, and , Rubin and Taylor. They gave the definition and first results and mentioned a lot of interesting open problems. If G graph, and f is a function that assigns to each verteof a positive integerwe say that is -choosable if, for every assignment of ets of integer) Z for all all number . in wiev Bollothe list chromatic number of any simple line graph does not . In chapter 7, we stud there is proper vertex coloring cThe graph is -choosable if it is f-choosable for the constant functio f(v)=k. The choice number of G, denoted , is the minimum integer so that is k-choosable. Obviously, this number is strictly larger than t, suggested independently by various researchers including
