The course is intended to provide a (reasonably high level) introduction to basic topics in graph theory, including:
matching theory and minimax theorems;
extremal graph theory, Ramsey theory, random graphs (some of this is also covered in 582-3, but we'll try to avoid a lot of overlap);
polyhedral issues if time allows.
Diestel, Graph Theory (Optional: most of what we cover will be in Diestel, but we won't really follow the book.)
The course is mostly self-contained, though some previous combinatorics, linear algebra, rudimentary probability are all occasionally helpful. See me if in doubt.