Introduction to graph theory

Introduction to Graph Theory
An introductory course from the School of Mathematics

This course aims to provide a thorough introduction to the subject of graph theory.

Course requirements
The following knowledge is required or desirable on commencement of study of this course:


 * knowledge of basic methods of proof
 * knowledge of basic probability

Course outline
This is an approximate depiction of the course:


 * Definitions
 * Bipartite Graphs
 * Hamilton Cycles and Eulerian Circuits
 * Planar Graphs
 * Statement of Kuratowski's Theorem
 * Matchings in Bipartite Graphs
 * Hall's Theorem
 * Connectivity
 * Menger's Theorem
 * Extremal Graph Theory
 * Hamilton and other cycles
 * Turan's Theorem
 * Ramsey's Theorem
 * Graph Colourings
 * Chromatic Polynomial
 * Vizing's Theorem
 * Four-Colour and Five-Colour Theorems
 * Extensions to other surfaces
 * Eigenvalues
 * Applications to Strongly Regular Graphs
 * The Probabilistic Method
 * Lower bounds for Ramsey numbers
 * Graphs with large girth and chromatic number

Lecture series

 * /Lecture 1/ Introduction and Definitions
 * /Lecture 2/ Bipartite Graphs and Trees
 * /Lecture 3/ Hamilton Cycles and Eulerian Circuits
 * /Lecture 4/ Graph Traversal
 * /Lecture 5/ Flows and Cuts
 * /Lecture 6/ Planar Graphs

List of Definitions

Assignments

 * /Problems 1/ (on Lectures 1-5)
 * /Problems 2/ (on Lectures 6-10)