Contents

• Introduction
• Graphs
• Flows, connectivity and matching
• Connectivity and the theorems of Menger
• Matchings
• Extremal graph theory
  • Complete subgraphs and Turán's theorem
  • The problem of Zarankiewicz
  
  
• Graph colouring
  • Vertex colouring and Brooks' theorem
  
  
• Edge colouring and Vizing's theorem
• Colouring graphs on surfaces
  • Plane graphs