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arXiv · 0802.2853

Discrete Jordan Curve Theorem: A proof formalized in Coq with hypermaps

Jean-François Dufourd
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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.

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Jean-François Dufourd. 2008-02-20. Discrete Jordan Curve Theorem: A proof formalized in Coq with hypermaps. https://arxiv.org/abs/0802.2853

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