Mac Lane’s Theorem for 3-Graphs

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 6 in The Foundations of Topological Graph Theory, 1995, pp 83-96 from Springer

Abstract: Abstract In this chapter, we give our first characterisation of planar graphs. This characterisation is due to Mac Lane. The basic idea is that a 2-connected graph is planar if and only if there is a family of circuits enjoying properties that we intuitively expect the boundaries of faces to have. The work in this chapter is in the more general setting of 3-graphs. Mac Lane’s theorem is deduced as a corollary. We conclude the chapter by obtaining another criterion due to Whitney.

Keywords: Planar Graph; Double Cover; Distinct Component; Boundary Space; Blue Edge (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-1-4612-2540-9_6

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