Special Math Lecture: Graph theory

A dinosaur
LecturerSerge RICHARD, Professor
DepartmentG30, 2020 Spring
Recommended for:Hu(J)・La(S)・Ec(S)・Sc(P・C・B)・En(P・C・Au)・Ag(B) (2.01.5 hours / session One session / week 15 weeks / semester)

Goals and Objectives of the Course

Graphs are playing an essential role in many fields, as for example in computer science, in optimization and in algorithmic complexity. Studying the abstract theory of graphs provides the tools for dealing with very diverse questions and with numerous applications.

During this course we shall study the abstract theory of finite graphs, and see extensions to infinite graphs. Applications will be considered according to the interest and to the motivation of the students.

Course Prerequisites

Basic knowledge on calculus and linear algebra, as provided in Calculus I & II and in Linear algebra I & II. Motivated 1st year students can also attend without these prerequisites but after a discussion with the instructor.

Course Contents/Plan

  1. The basics
  2. Representations and structures
  3. Trees
  4. Spanning trees
  5. Connectivity
  6. Optimal traversals
  7. Graph colorings
  8. Directed graphs
  9. Flows
  10. Random graphs
  11. The configuration model
  12. Epidemics on graphs

Course Evaluation Methods

The final grade will be based on the active participation during the lectures and on some written reports. Computer implementations of some exercises will accepted as reports.

Notice for Students

It is expected that the students will show a certain maturity in studying independently and in choosing some exercises and problems to solve. Study sessions will be organized on a weekly basis.
This course in an optional subject which does not count towards the number of credits required for graduation in any program at Nagoya University.


Free reference books will be provided during the lectures

Reference Book

Free reference books will be provided during the lectures


Last updated

December 17, 2020