School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2020/21 Last Updated: 25 February 2021

MAT-30001 - Graph Theory

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This module introduces the concept of a graph as a pictorial representation of a symmetric relation. A variety of topics are investigated and, for each one, at least one of the major theorems is proved. The emphasis is on pure graph theory although some applications are explored via worked examples and coursework.

The aim of this module is to study various topics in graph theory, together with a number of applications.

recognise, and establish properties, of different types of graphs such as trees, bipartite and complete graphs: 1,2

prove, and apply, conditions for a graph to be Eulerian or Hamiltonian: 1,2

prove, and apply, results related to the colouring of the vertices or edges of a graph: 1,2

prove, and apply, results related to properties of extremal graphs: 2

prove, and apply, results concerning planar graphs: 2

prove, and apply, conditions for a graph to be Eulerian or Hamiltonian: 1,2

prove, and apply, results related to the colouring of the vertices or edges of a graph: 1,2

prove, and apply, results related to properties of extremal graphs: 2

prove, and apply, results concerning planar graphs: 2

Learning/teaching comprises 30 hours video lectures, 5 hours flipped examples classes, and 2 hours final exam.

Independent study comprises 30 hours examples class preparation, 10 hours for completion of assignment, 20 hours preparation for examination, and 53 hours consolidation of lecture material.

Independent study comprises 30 hours examples class preparation, 10 hours for completion of assignment, 20 hours preparation for examination, and 53 hours consolidation of lecture material.

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On-line, take-home assignment

One take-home, written assignments to be completed on-line. The assignment consists of a set of questions with pre-allocated space for written solutions which will be uploaded to the KLE. Students should expect to spend 10 hours on the assessment.

On-line, open book examination

The examination paper will consist of no less than five and not more than eight questions all of which are compulsory. In response to Covid, the examination will be online and open book. A well-prepared student should expect to complete the assessment in two hours.