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