Type of Document Master's Thesis Author Baber, Courtney Leigh Author's Email Address clbaber@vt.edu URN etd-06082009-155312 Title An Introduction to List Colorings of Graphs Degree Master of Science Department Mathematics Advisory Committee

Advisor Name Title Brown, Ezra A. Committee Chair Rossi, John F. Committee Member Shimozono, Mark M. Committee Member Keywords

- channel assignment problem
- list coloring
- graph
Date of Defense 2009-04-30 Availability unrestricted AbstractOne of the most popular and useful areas of graph theory is graph colorings. A graphcoloring 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 Erd˝os, 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.

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