An introductory course from the School of Mathematics
This course aims to provide a thorough introduction to the subject of graph theory.
The following knowledge is required or desirable on commencement of study of this course:
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
- Connectivity
- 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
List of Definitions