Discrete mathematics - Graph theory and algorithms

Teacher(s)

Blondel Vincent; Delvenne Jean-Charles;

Language

French

Main themes

Introduction to the language and theory of graphs : questions of characterization, isomorphism, existence and enumeration. Properties of directed and undirected graphs such as connectivity, planarity, k-colorability and the property of being Eulerian, perfect, etc. Modelling of practical problems : data structures and algorithms for the exploration of graphs. Basic graph algorithms and an analysis of their complexity.

Aims

At the end of this learning unit, the student is able to :
1	AA1 : 1,2,3 More precisely, by the end of the course the student will be able to : model various problems in the language of graph theory identify if a graph-theoretic problem has a known efficent algorithmic solution or not propose and apply an algorithm to solve sucha a problem, at least for some classes of graphs prove in a clear and rigorous fashion elementary properties related to the concepts covered in the course

Content

Structure and characterisation of graphs - basic concepts - degree, connected components, path, cycle, cut, minor, etc. Classes of graphs and their recognition - perfect, series parallel, planar graphs, acyclic digraphs, etc. Exploration of graphs and tests of their properties - k-connected, Eulerian, etc. Flows - theorems of Menger and Hall, maximum flow and minimum cost flow algorithms and their complexity. Problems : finding optimal matchings and stable sets, the travelling salesman problem, cut, graph partitioning and graph colouring problems

Teaching methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

The course is organised in lessons and supervised exercise sessions.

Evaluation methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

The students are evaluated through small projects during the semester and through a written (or possibly oral depending on the circumstances) exam, based on the specific objectives described above.

Online resources

Moodle page of the course

Bibliography

Ouvrage de base (non obligatoire) / primary (non mandatory) reference :
Graph Theory with Applications, A. Bondy- U.S.R. Murty, Springer, téléchargement libre/free download
Aussi /also :

• Algorithmic Graph Theory, Alan Gibbons, Cambridge University Press 1985
• Introduction to Graph Theory, Douglas West, Prentice Hall 1996.
• Combinatorial Optimization, W.R. Cook et al., Wiley 1998.
• Network Flows, Ahuja et al., Prentice Hall 1993.

Teaching materials

• Notes de cours/lectures notes
• Transparents/slides

Faculty or entity

MAP