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Discrete Jordan Curve Theorem: A proof formalized in Coq with hypermaps
Published 20 Feb 2008 in cs.LO and cs.DM | (0802.2853v1)
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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