
We give a systematic
introduction to some core areas of combinatorics and graph theory,
with special emphasis on links between seemingly unrelated areas
and on applications to problems in other parts of mathematics
and computer science. Some basic knowledge of combinatorics,
linear algebra, and calculus are required.
We cover the following
topics:
 Chromatic number vs. clique number, perfect graphs
 Coloring algorithms, greedy and probabilistic
 Graph minors, Hadwigers's conjecture, Hajós theorem
 Large topological minors in dense graphs
 Menger's theorem, KonigHall theorems, connectivity
 LiptonTarjan separator theorem, divideandconquer
 Applications of linear algebra
 Combinatorial designs
Recommended Textbooks
R. Diestel: Graph Theory, Springer, 1997, 2000.
B. Bollobás: Modern Graph Theory, Springer, 1998.
S. Jukna: Extremal Combinatorics, Springer, 2001.

