Digital Jordan Curve Theorems

  • Christer O. Kiselman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1953)

Abstract

Efim Khalimsky’s digital Jordan curve theorem states that the complement of a Jordan curve in the digital plane equipped with the Khalimsky topology has exactly two connectivity components. We present a new, short proof of this theorem using induction on the Euclidean length of the curve. We also prove that the theorem holds with another topology on the digital plane but then only for a restricted class of Jordan curves.

Keywords

Topological Space Jordan Curve Euclidean Plane Adjacent Point Connected Subset 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Christer O. Kiselman
    • 1
  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

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