|
Topic
|
No. of hours
|
Lecture
|
Tutorial/ Practical
|
|
Basics – definitions and basic facts.
|
6
|
3
|
3
|
|
basic examples; elementary properties of graphs.
|
6
|
3
|
3
|
|
Trees , forests, Euler tours.
|
6
|
3
|
3
|
|
Early highlights such as the Handshaking Lemma; graph isomorphism.
|
6
|
3
|
3
|
|
Matching, covering, packing.
|
6
|
3
|
3
|
|
special graph classes, e.g. complete graphs, paths, cycles.
|
6
|
3
|
3
|
|
Connectivity, Menger's Theorem.
|
6
|
3
|
3
|
|
planar graphs, trees; characterizations of trees.
Connections between groups and graphs.
|
6
|
3
|
3
|
|
Planar graphs, Kuratowski's Theorem.
|
6
|
3
|
3
|
|
Coloring (vertex coloring, edge coloring, 4-color theorem…).
|
6
|
3
|
3
|
|
Infinite graphs, paths, trees.
|
6
|
3
|
3
|
|
Ramsey Theory.
|
6
|
3
|
3
|
|
Hamiltonian cycles.
|
6
|
3
|
3
|
|
Random graphs.
|
6
|
3
|
3
|
