Topics in Discrete Mathematics

Welcome to the unofficial page for the Graph Theory section of Topics in Discrete Mathematics! This material is part of a course at the University of Bristol (MATH30002 at level H, MATHM0009 at level M), and copyright should be considered to reside with them. Bristol students should refer to blackboard in the first instance, but this page will act as a mirror for some content.

Warm-up Activity
Please try playing with the app One Touch Drawing, which is freely available for android and iThings.

Lecture Notes
The complete notes are now available. The material covered is as follows:

  • Section 1- Introduction.
  • Section 2- Basic definitions.
  • Section 3- Eulerian trails and tours.
  • Section 4- Hamiltonian Paths and Cycles, Trees.
  • Section 5- Adjacency Matrices.
  • Section 6- Planar Graphs.
  • Section 7- Structural Balance.

The notes are here (caution: 10MB PDF).

Lecture Slides
Here are handout versions of the slides, for easier printing.

  • Lecture 1: Sections 1,2,3 and 4 (up to example low-degree graphs with Hamiltonian cycles).
  • Lecture 2: Completion of of section 4 (proof of Dirac’s Theorem, trees), start of section 5 (adjacency matrices).
  • Lecture 3: Completion of section 5 (adjacency matrices).
  • Lecture 4: Section 6 (planarity).
  • Lecture 5: Section 7 (structural balance).

Problem Sheet
This (and solutions, later on) will only be available through blackboard.

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