5 credits
30.0 h + 22.5 h
Q1
Teacher(s)
Blondel Vincent; Delvenne JeanCharles; Jungers Raphaël (compensates Blondel Vincent);
Language
French
Prerequisites
This courses assumes that the elementary notions of discrete mathematics are acquired such as taught in LEPL1108.
The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
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, kcolorability 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 :

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Content
Structure and characterization 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  kconnected, 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
The course is organized in lessons and supervised exercise sessions.
Evaluation methods
The students are evaluated individually through a written exam based on the specific objectives described above.
Online resources
Bibliography
Ouvrage de base :
Syllabus sur moodle
Aussi :
Syllabus sur moodle
Aussi :
 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.
Faculty or entity
MAP
Programmes / formations proposant cette unité d'enseignement (UE)
Title of the programme
Sigle
Credits
Prerequisites
Aims
Master [120] in Computer Science and Engineering
Master [120] in Electrical Engineering
Master [120] in Statistic: General
Master [120] in Computer Science
Minor in Engineering Sciences: Applied Mathematics
Additionnal module in Mathematics