Abstract. This paper presents a formalized proof of a discrete form of the Jordan Curve Theorem. It is based on a hypermap model of planar subdivisions, formal specifications and proofs assisted by the Coq system. Fundamental properties are proven by structural or noetherian induction: Genus Theorem, Euler's Formula, constructive planarity criteria. A notion of ring of faces is inductively defined and a Jordan Curve Theorem is stated and proven for any planar hypermap.
In 2009, Dufourd formally verified a constructive proof of the Discrete Jordan Curve Theorem REF , based on hypermaps.
Discrete Jordan Curve Theorem: A proof formalized in Coq with hypermaps
Dans Proceedings of the 25th Annual Symposium on the Theoretical Aspects of Computer Science - STACS 2008, Bordeaux : France (2008)
Mathematics Computer Science