Undergraduate Course: Combinatorics and Graph Theory (MATH10072)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 10 (Year 3 Undergraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  A first course in combinatorics and graph theory: graphs, Euler's VE+F=2 theorem, Kuratowski's theorem, colourings of graphs, matching, Hall's marriage theorem, applications 
Course description 
Typical course contents might include the following: Graphs, digraphs, paths and cycles: Eulerian and Hamiltonian graphs, connectivity, adjacency matrices. Applications: shortest path problem, critical path problem, Guan¿s postman problem, travelling salesman problem.
Trees: properties, counting trees, minimum connector problem and other applications.
Planar graphs, Kuratowski¿s theorem, Euler's VE+F=2 theorem, dual graphs.
Vertexcolourings, edgecolourings, and facecolourings of graphs, chromatic polynomials, fourcolour theorem.
Matching, Hall's marriage theorem, Menger¿s theorem, maxflow mincut theorem and application to network flow problems.

Information for Visiting Students
Prerequisites  Equivalence relations, permutations, set theory, group theory, binomial coefficients. Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2024/25, Available to all students (SV1)

Quota: None 
Course Start 
Semester 1 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 20%, Examination 80% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)  Combinatorics and Graph Theory (MATH10072)  2:120  
Learning Outcomes
On completion of this course, the student will be able to:
 Identify properties of graphs (such as Eulerian/Hamiltonian/Planar/Bipartite/Connectivity/Colourablity).
 Write proofs based on properties of graphs.
 Solve application problems (such as the shortest path problem, critical path problem, Guan¿s postman problem, minimum connector problem, network flow problems).
 Make computations associated to graphs.

Reading List
Reference books which contain some material relevant to the course:
* A First Course in Combinatorial Mathematics by Ian Anderson
* Aspects of Combinatorics by Victor Bryant.
* Graphs An Introductory Approach, by R J Wilson and J J Watkins
* Introduction to Graph Theory, by R J Wilson 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  CGT 
Contacts
Course organiser  Dr Ana Rita Pires
Tel: (0131 6)50 5079
Email: apires@ed.ac.uk 
Course secretary  Miss Greta Mazelyte
Tel:
Email: greta.mazelyte@ed.ac.uk 

