MATHS 715 : Graph Theory and Combinatorics


2021 Semester One (1213) (15 POINTS)

Course Prescription

A study of combinatorial graphs (networks), designs and codes illustrating their application and importance in other branches of mathematics and computer science.

Course Overview

This course is intended for students who have enjoyed the introduction to abstract algebra and parts of discrete mathematics presented in MATHS 254 or 255 and MATHS 320, 326 or 328. The main focus of the course is on combinatorial structures, especially graphs and their properties. Emphasis is placed on the contexts in which these structures occur, methods by which they can be modelled and analysed, and their diverse applications. We introduce students to a wide variety of aspects of the subject and some of its major theorems. A student completing this course will have a wide knowledge of fundamentals and approaches in this eld of growing importance.

Course Requirements

Prerequisite: B+ pass in MATHS 326 or 320

Capabilities Developed in this Course

Capability 1: Disciplinary Knowledge and Practice
Capability 2: Critical Thinking
Capability 3: Solution Seeking
Capability 4: Communication and Engagement
Capability 5: Independence and Integrity

Learning Outcomes

By the end of this course, students will be able to:
  1. Demonstrate familiarity and confidence in using the definitions and tools of graph theory and combinatorics, as well as tools from linear algebra and fundamental concepts of discrete mathematics, to answer questions and solve theoretical problems in these fields (Capability 1, 2 and 3)
  2. Derive properties of graphs and other combinatorial structures from their fundamental axioms, and draw conclusions from these properties (Capability 1, 2 and 5)
  3. Develop clear and concise proofs of important fundamental theorems in graph theory and combinatorics, and to communicate these effectively in written form (Capability 4 and 5)
  4. Generate and describe examples of graphs and other combinatorial structures satisfying given feasible conditions (Capability 1, 2, 3, 4 and 5)


Assessment Type Percentage Classification
Assignments 30% Individual Coursework
Test 20% Individual Test
Final Exam 50% Individual Examination
Assessment Type Learning Outcome Addressed
1 2 3 4
Final Exam
A student's final mark (out of 100) will be determined by the maximum of the following two options:
1) 30 marks from Assignments, 20 marks from the Test, 50 marks from the Final Exam
2) 100 marks from the Final Exam.
Every student needs to score at least 35% in the Final Exam to pass the course.


There is no additional Tuākana support for this course

Key Topics

This course will cover a selection of topics involving theory and applications of graphs (networks) and other aspects of combinatorics.  These topics include graph connectivity, trees, colourings, embeddings, matchings, eigenvalue methods, among others. 

Special Requirements

A good background in basic linear and abstract algebra is assumed, and also some knowledge of graphs and other discrete structures (e.g. from CompSci 225 or Maths 326) could be helpful.  There are no special requirements such as practical work, evening tests or field trips for this course.

Workload Expectations

This course is a standard 15 point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in.

For this course, each week you can expect 3 hours of lectures, 3 hours of reading and thinking about the content and 4 hours of work on assignments and/or preparation for the test or final exam.

Delivery Mode

Campus Experience

Activities for the course are scheduled in a standard weekly timetable.  Attendance is recommended at lectures, which will not be available as recordings (unless the campus is closed and lectures have to be delivered online). There are no tutorials or group discussions. Attendance on campus is required for the Test (unless the campus is closed and the Test has to be undertaken online). Attendance on campus is required for the Final Exam (unless the campus is closed and the Final Exam has to be undertaken online).

Learning Resources

There is no text book, but a set of course notes will be made available on Canvas. There is also a broad collection of books in the library on the course topics, as well as plenty of online resources.

Student Feedback

During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.

At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback.

Your feedback helps to improve the course and its delivery for all students.

Digital Resources

Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).

Please remember that the recording of any class on a personal device requires the permission of the instructor.

Academic Integrity

The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed against online source material using computerised detection mechanisms.


The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.

You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.

Inclusive Learning

All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.

Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website

Special Circumstances

If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.

If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page

This should be done as soon as possible and no later than seven days after the affected test or exam date.

Learning Continuity

In the event of an unexpected disruption we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and your assessment is fair, and not compromised. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator, and if disruption occurs you should refer to the University Website for information about how to proceed.

The following apply with regard to Covid Alert Levels:
Level 1:  Delivered normally as specified in delivery mode.
Level 2: You will not be required to attend in person.  All teaching and assessment will have a remote option.
Level 3 or 4: All teaching activities and assessments are delivered remotely.

Student Charter and Responsibilities

The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter


Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.

In this course you may be asked to submit your coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published.

Published on 16/02/2021 10:52 a.m.