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

Jean-François Dufourd (1)

1 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection

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.

Mots clés: Formal specifications; Computational topology; Computer-aided proofs; Coq; Planar subdivisions; Hypermaps; Jordan Curve Theorem

Domaines: Logique en informatique [cs.LO]; Mathématique discrète [cs.DM]

Jean-François Dufourd. Discrete Jordan Curve Theorem: A proof formalized in Coq with hypermaps. STACS 2008, Feb 2008, Bordeaux, France. pp.253-264. ⟨hal-00221501⟩