Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 42, No. 2, pp. 307-311 (2001)

Simple Polygons with an Infinite Sequence of Deflations

Thomas Fevens, Antonio Hernandez, Antonio Mesa, Patrick Morin, Michael Soss, Godfried Toussaint

School of Computer Science, McGill University, 3480 University Street, Montreal, Quebec Canada H3A 2A7 e-mail:

Abstract: Given a simple polygon in the plane, a deflation is defined as the inverse of a flip in the Erdos-Nagy sense. In 1993 Bernd Wegner conjectured that every simple polygon admits only a finite number of deflations. In this note we describe a counter-example to this conjecture by exhibiting a family of polygons on which deflations go on forever.

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