Math 275 - Graph Theory

A graph is a set of points (called vertices) with some connections
(called edges) between them.  They are particularly helpful in
understanding the behavior of networks but they can arise in many
different contexts, both theoretical and applied.  The theorems and
techniques developed in the course are useful in electrical engineering,
operations research, and computer science among other areas.  They are
also incredibly interesting in and of themselves.

In this course we will study various properties of graphs.  We will
analyze how easy they are to disconnect.  We will consider when they
have closed paths that go through all of their vertices. These are
called Hamiltonian cycles and are closely related to the Traveling
Salesman Problem.  We will also consider how many different colors are
needed to color the vertices so that no two vertices of the same color
have an edge between them.  This problem is the general case of the Four
Color Theorem, a problem first discussed in the mid-19th century
but now relevant to the assigning of cell phone frequencies. 

This course is suitable for upper-level undergraduates as well as
graduate students in mathematics and engineering.