Duality

C. Paul Bonnington and Charles H. C. Little
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C. Paul Bonnington: University of Auckland, Department of Mathematics
Charles H. C. Little: Massey University, Department of Mathematics

Chapter 8 in The Foundations of Topological Graph Theory, 1995, pp 111-141 from Springer

Abstract: Abstract The concept of a gem, as we have seen, corresponds closely to the idea of an imbedding of a map but is much simpler conceptually. It will also prove to be of theoretical assistance to us in this chapter. We use it to illuminate the notion of duality, which manifests itself topologically as a relationship between vertices and faces. Following the treatment in Lins (1982), we show that this relationship is merely the tip of the iceberg — there are actually three dualities. This work leads naturally to the principal edge tripartition of a graph, studied by Rosenstiehl and Read (1978), and culminates in another characterisation of planar graphs.

Date: 1995
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DOI: 10.1007/978-1-4612-2540-9_8

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