# 2009/10 Undergraduate Module Catalogue

## MATH3032 Graph Theory

### 10 creditsClass Size: 200

**Module manager:** Professor B Cooper**Email:** s.b.cooper@leeds.ac.uk

**Taught:** Semester 1 View Timetable

**Year running** 2009/10

### Pre-requisites

MATH2210 | Introduction to Discrete Mathematics |

**This module is approved as an Elective**

### Module summary

This module provides an introduction to the basic ideas such as connectedness, trees, planar graphs, Eulerian and Hamiltonian graphs, directed graphs and the connection between graph theory and the four colour Problem. Graph theory is an important mathematical tool in such different areas as linguistics, chemistry and, especially, operational research. This module will include some abstract proofs.### Objectives

To introduce students to some of the main concepts of graph theory.On completion of this module, students should be able to:

(a) identify basic examples of isomorphic and non-isomorphic pairs of graphs, and make simple deductions involving vertex degrees;

(b) apply a selection of criteria related to Eulerian and Hamiltonian graphs;

(c) explain and apply the basic theories for trees, planar graphs and directed graphs;

(d) show a basic knowledge of graph colourings, and apply a range of techniques for identifying chromatic numbers for graphs and surfaces.

### Syllabus

Topics chosen from:

1. Basic definitions. Adjacency matrices, connected graphs, vertex degrees.

2. Eulerian graphs and applications.

3. Hamiltonian graphs. Dirac's theorem.

4. Trees. Cayley's Theorem.

5. Planar graphs. Euler's theorem, Kuratowski's theorem (without proof).

6. Digraphs. Robbins' Theorem, tournaments.

7. Graph colourings. The five-colour theorem for planar graphs, the four-colour theorem for planar graphs (without proof). Brook's Theorem.

8. Chromatic numbers of surfaces, Heawood's inequality.

### Teaching methods

Delivery type | Number | Length hours | Student hours |

Example Class | 11 | 1.00 | 11.00 |

Lecture | 22 | 1.00 | 22.00 |

Private study hours | 67.00 | ||

Total Contact hours | 33.00 | ||

Total hours (100hr per 10 credits) | 100.00 |

### Methods of assessment

**Coursework**

Assessment type | Notes | % of formal assessment |

In-course Assessment | . | 15.00 |

Total percentage (Assessment Coursework) | 15.00 |

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

**Exams**

Exam type | Exam duration | % of formal assessment |

Standard exam (closed essays, MCQs etc) | 2 hr | 85.00 |

Total percentage (Assessment Exams) | 85.00 |

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

### Reading list

The reading list is available from the Library websiteLast updated: 22/03/2010

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- Undergraduate module catalogue
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- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue

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