# MTH4151 - Advanced graph theory - 2019

## 6 points, SCA Band 2, 0.125 EFTSL

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Chief examiner(s)

Coordinator(s)

Unit guides

Offered

Clayton

• First semester 2019 (On-campus)

Prerequisites

Enrolment in the Master of Mathematics

MTH3170

Prohibitions

MTH5151

Notes

This unit is offered in alternate years commencing S1, 2019

## Synopsis

Networks are ubiquitous and fundamental in the modern world, whether they are computer networks, transport networks, food webs, polymer chains, social networks and so on. Graph theory is the mathematics of networks. Familiarity with the basic notions and terminology will be assumed and built on to give an advanced understanding of a number of topics chosen from the following list: random graph theory, probabilistic method, extremal graph theory, Ramsey theory, advanced algorithms, combinatorial optimisation, geometric graph theory, topological graph theory, structural graph theory, algebraic graph theory, graph colouring, matroid theory.

## Outcomes

On completion of this unit students will be able to:

1. Formulate complex problems using appropriate graph-theoretic terminology.
2. Appreciate the role of graph theory in other areas of mathematics.
3. Apply sophisticated mathematical methods in the setting of graph theory.
4. Apply sophisticated graph-theoretic arguments in a variety of settings.
5. Communicate complex information about graphs.
6. Apply critical thinking in the field of graph theory.
7. Read, understand and verify expert mathematical proofs about graphs.
8. Develop and write mathematical proofs about graphs.
9. Understand several real-world applications of graph theory.

## Assessment

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.