This is a junior-senior level course in graph theory, and other non-enumerative aspects of combinatorics. The graphs studied in this class are networks composed of nodes or vertices and arcs or edges connecting them. They are often used to model varioius discrete situations and problems, often involving optimization.
The course assumes that the student has taken single-variable calculus, as well as linear algebra (e.g. determinants occasionally come up). Precise statements and theorems are a part of this class, and it is assumed that the students can prove things, rigorously.
Topics often include Euler and Hamiltonian circuits, degree sequences, spanning trees, network flows, bipartite matchings, graph coloring, planar graphs.
Other non-enumerative combinatorial topics that are occasionally taught in the course include design theory, latin squares and coding theory.
Due to some of the mildly algebraic aspects of the class, it is among those that can be counted toward a math major's algebra requirement (part of "Column Y") as described here .
Note that Math 4707 is class which covers some of the material of Math 5707 at a slightly lower-level, as well as some of the graph theory covered in Math 5705.
To suggest some flavor of Math 5707, a student might learn how to ...