Program of

Mathematical Methods (part A)

for the "Laurea Magistrale" MASSET

(Prof. M. Ferri)


The very nice team of acad. year 2009-2010!

(Part of) the very nice team of academic year 2009-2010.

The class of academic year 2008-1009 was nice too!


The course consists of two parts. Part A is dedicated to Graph Theory. Part B is held by Prof. Giovanna Citti Ph.D.

Theory

1. Graphs and subgraphs (1.1 to 1.8).
2. Trees (2.1; 2.2 up to Cor. 2.4.2; 2.3 to 2.5).
3. Connectivity (3.1).
4. Euler tours and Hamilton cycles (4.1; 4.2 up to Thm. 4.2; 4.3 up to Fleury'alg.; 4.4 first 11 lines).
5. Matchings (5.1).
6. Edge colourings (6.1 without lemmas; 6.2: Thm. 6.2; 6.3 first 21 lines).
8. Vertex colourings (8.1 up to Cor. 8.1.2; 8.2; 8.3 up to Thm. 8.5; 8.4; 8.6 first 10 lines).
9. Planar graphs (9.1; 9.2; 9.3: Thm. 9.5, Cors. 9.5.4, 9.5.5; 9.5: Thm. 9.10; 9.6: Thm. 9.11 and footnote at page 157).
10. Directed graphs (10.1; 10.2 up to Cor. 10.1).

Exercises

Modelling problems with graphs. Writing matrices associated with graphs. Computing graph invariants. Solving elementary graph problems.

Textbooks

Official textbook:

J.A. Bondy and U.S.R. Murty, "Graph theory with applications",
North Holland, 1976.
Freely downloadable at http://www.ecp6.jussieu.fr/pageperso/bondy/books/gtwa/gtwa (24 MB).

Support textbooks:

J.A. Bondy and U.S.R. Murty, "Graph theory",
Springer Series: Graduate Texts in Mathematics, Vol. 244 (2008)

R. Diestel, "Graph theory", Springer Series: Graduate Texts in Mathematics, Vol. 173 (2005)
Freely downloadable at http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/GraphTheoryIII.counted.pdf (3 MB).

Supplementary material:

Test of Dec. 4, 2008 and its solution.
Test of Jan. 26, 2009 and its solution.

Projected slides: Smallworld (0.2 MB), Configuration spaces (7.8 MB).

Have a look at the demos of graph theory.