Non-separating Curves in Surfaces

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 5 in The Foundations of Topological Graph Theory, 1995, pp 63-81 from Springer

Abstract: Abstract An important theorem of topology asserts that the first Betti number of a surface is the largest number of closed curves that can be drawn in the surface without dividing it into two or more regions. We now generalise this theorem (which is itself a generalisation of the Jordan curve theorem) to 3-graphs. The topological implications of our results are discovered by specialising the main theorems to the case of gems.

Keywords: Betti Number; Closed Curf; Boundary Space; Terminal Vertex; Blue Edge (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-1-4612-2540-9_5

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