Graph Theory

The details
Mathematical Sciences
Colchester Campus
Postgraduate: Level 7
Sunday 15 January 2023
Friday 24 March 2023
04 May 2022


Requisites for this module



Key module for


Module description

This module introduces graph theory and some key definitions, proofs and proof techniques associated with graph theory. It is distinguished from the undergraduate version of the module by greater emphasis on the concept of proof.

Module aims

1. To introduce students to basic definitions and results of graph theory.
2. To develop students’ advanced understanding of some main proofs in graph theory.
3. To develop understanding of how to apply such results in particular problems at an advanced level.

Module learning outcomes

1. Give basic graph theoretic definitions.
2. Prove basic results in the theory of graphs.
3. Show critical understanding of some results about matchings (Hall’s theorem and equivalent results).
4. Have critical understanding of some basic results about Hamilton cycles.
5. Have experience of problems connected with chromatic number, and know basic theory and how to apply it.
6. Have critical understanding of extremal graph theory, Ramsey theory and the theory of random graphs.
7. Advanced understanding of proofs of key theorems in the theory of graphs.

Module information

TTeaching in the department will be delivered using a range of face to face lectures, classes and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.

Learning and teaching methods

Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support. Specific to the PGT students there will be additional lectures emphasising proof. Students having issues with the module are encouraged to talk to the module supervisor during office hours/open-door policy.


The above list is indicative of the essential reading for the course.
The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students.
Further reading can be obtained from this module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Exam  Main exam: In-Person, Closed Book, 120 minutes during Summer (Main Period) 
Exam  Reassessment Main exam: In-Person, Closed Book, 120 minutes during September (Reassessment Period) 

Additional coursework information

Formative problem sheets will be provided, and discussed in some of the lectures.

Exam format definitions

  • Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
  • In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
  • In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
  • In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Your department will provide further guidance before your exams.

Overall assessment

Coursework Exam
0% 100%


Coursework Exam
0% 100%
Module supervisor and teaching staff
Dr Alexei Vernitski, email:
Dr Alexei Vernitski



External examiner

Prof Stephen Langdon
Brunel University London
Available via Moodle
Of 11 hours, 7 (63.6%) hours available to students:
4 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s), module, or event type.


Further information
Mathematical Sciences

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