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Non-separating Curves in Surfaces

In: The Foundations of Topological Graph Theory

Author

Listed:
  • C. Paul Bonnington

    (University of Auckland, Department of Mathematics)

  • Charles H. C. Little

    (Massey University, Department of Mathematics)

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.

Suggested Citation

  • C. Paul Bonnington & Charles H. C. Little, 1995. "Non-separating Curves in Surfaces," Springer Books, in: The Foundations of Topological Graph Theory, chapter 5, pages 63-81, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2540-9_5
    DOI: 10.1007/978-1-4612-2540-9_5
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