List Coloring Problems

Abstract

A list assignment L of a graph G is a function which assigns a set of colors to all vertices and G is called L-colorable if each vertex v can be colored by using color from L(v) and adjacent vertices receive distinct colors.
In this article, definitions related to list assignment problems are introduced. Then some research of list assignment problems is proposed; for example, a characterization of 2-choosable graphs, a characterization of 3-choosable complete bipartite graphs and a list assignment such that prevents K_7,7 and K_7,8 from being 3-choosable. Finally, topics of possible future research
are presented.