Planarity

Planarity is one of the classical topics in graph theory, partly due to the celebrated 4-colour theorem which largely fostered the development of graph theory. This theorem will be discussed in the next chapter, whilst this chapter will focus solely on the planarity property. As a blending of combinatorics and topology, there are some topological preliminaries which are necessary, but these will not be discussed too deeply. The central result in this chapter is Kuratowski’s theorem, which characterises planar graphs in terms of forbidden minors. This is a result with deep extensions in graph theory.