# An Introduction to List Colorings of Graphs

Abstract (Summary)

One of the most popular and useful areas of graph theory is graph colorings. A graph
coloring is an assignment of integers to the vertices of a graph so that no two adjacent
vertices are assigned the same integer. This problem frequently arises in scheduling and
channel assignment applications. A list coloring of a graph is an assignment of integers
to the vertices of a graph as before with the restriction that the integers must come from
specific lists of available colors at each vertex. For a physical application of this problem,
consider a wireless network. Due to hardware restrictions, each radio has a limited set of
frequencies through which it can communicate, and radios within a certain distance of each
other cannot operate on the same frequency without interfering. We model this problem as
a graph by representing the wireless radios by vertices and assigning a list to each vertex
according to its available frequencies. We then seek a coloring of the graph from these lists.
In this thesis, we give an overview of the last thirty years of research in list colorings. We
begin with an introduction of the list coloring problem, as defined by ErdËos, Rubin, and
Taylor in [6]. We continue with a study of variations of the problem, including cases when
all the lists have the same length and cases when we allow different lengths. We will briefly
mention edge colorings and overview some restricted list colors such as game colorings and
L(p, q)-labelings before concluding with a list of open questions.
Bibliographical Information:

Advisor:John Rossi; Mark Shimozono; Ezra Brown

School:Virginia Polytechnic Institute and State University

School Location:USA - Virginia

Source Type:Master's Thesis

Keywords:mathematics

ISBN:

Date of Publication:06/11/2009