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 Lecture 7 not available yet Lecture 8 not available yet Lecture 9 not available yet Lecture 10 not available yet Lecture 11 not available yet Lecture 12 not available yet Lecture 13 not available yet Lecture 14 not available yet Lecture 15 not available yet Lecture 16 not available yet Lecture 17 not available yet Lecture 18 not available yet Lecture 19 not available yet Lecture 20 not available yet Lecture 21 not available yet Lecture 22 not available yet Lecture 23 not available yet Lecture 24 not available yet Lecture 25 not available yet Lecture 26 not available yet Lecture 27 not available yet Lecture 28 not available yet Lecture 29 not available yet Lecture 30 not available yet List of Definitions Assignments Problems 1 (on Lectures 1-5) not available yet Problems 2 (on Lectures 6-10) not available yet Problems 3 (on Lectures 11-15) not available yet Problems 4 (on Lectures 16-20) not available yet Problems 5 (on Lectures 21-25) not available yet Problems 6 (on Lectures 26-30) not available yet Examinations not available yet Recommended student evaluation scheme not available yet